Mynhardt, Kieka; Neilson, Linda Comparing upper broadcast domination and boundary independence broadcast numbers of graphs. (English) Zbl 07809337 Trans. Comb. 13, No. 1, 105-126 (2024). MSC: 05C69 PDFBibTeX XMLCite \textit{K. Mynhardt} and \textit{L. Neilson}, Trans. Comb. 13, No. 1, 105--126 (2024; Zbl 07809337) Full Text: DOI
Brewster, Richard; Mynhardt, Kieka; Teshima, Laura The Realizability of Theta Graphs as Reconfiguration Graphs of Minimum Independent Dominating Sets. arXiv:2305.17814 Preprint, arXiv:2305.17814 [math.CO] (2023). MSC: 05C69 BibTeX Cite \textit{R. Brewster} et al., ``The Realizability of Theta Graphs as Reconfiguration Graphs of Minimum Independent Dominating Sets'', Preprint, arXiv:2305.17814 [math.CO] (2023) Full Text: arXiv OA License
Hoepner, Jules; MacGillivray, Gary; Mynhardt, Kieka Boundary and Hearing Independent Broadcasts in Graphs and Trees. arXiv:2305.03516 Preprint, arXiv:2305.03516 [math.CO] (2023). MSC: 05C69 BibTeX Cite \textit{J. Hoepner} et al., ``Boundary and Hearing Independent Broadcasts in Graphs and Trees'', Preprint, arXiv:2305.03516 [math.CO] (2023) Full Text: arXiv OA License
Brewster, R. C.; Mynhardt, C. M.; Teshima, L. E. The \(i\)-Graphs of Paths and Cycles. arXiv:2303.08190 Preprint, arXiv:2303.08190 [math.CO] (2023). MSC: 05C69 BibTeX Cite \textit{R. C. Brewster} et al., ``The $i$-Graphs of Paths and Cycles'', Preprint, arXiv:2303.08190 [math.CO] (2023) Full Text: arXiv OA License
Brewster, R. C.; Mynhardt, C. M.; Teshima, L. E. Reconfiguration of Minimum Independent Dominating Sets in Graphs. arXiv:2303.06299 Preprint, arXiv:2303.06299 [math.CO] (2023). MSC: 05C69 BibTeX Cite \textit{R. C. Brewster} et al., ``Reconfiguration of Minimum Independent Dominating Sets in Graphs'', Preprint, arXiv:2303.06299 [math.CO] (2023) Full Text: arXiv OA License
MacGillivray, Gary; Mynhardt, C. M.; Virgile, Virgélot Eternal domination and clique covering. (English) Zbl 1499.05477 Electron. J. Graph Theory Appl. 10, No. 2, 603-624 (2022). MSC: 05C69 PDFBibTeX XMLCite \textit{G. MacGillivray} et al., Electron. J. Graph Theory Appl. 10, No. 2, 603--624 (2022; Zbl 1499.05477) Full Text: DOI arXiv
Mynhardt, C. M.; Roux, A. Irredundance graphs. (English) Zbl 1498.05188 Discrete Appl. Math. 322, 36-48 (2022). MSC: 05C60 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{A. Roux}, Discrete Appl. Math. 322, 36--48 (2022; Zbl 1498.05188) Full Text: DOI arXiv
Mynhardt, C. M.; Roux, A. Irredundance trees of diameter 3. (English) Zbl 1497.05061 Discrete Math. 345, No. 12, Article ID 113079, 10 p. (2022). MSC: 05C12 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{A. Roux}, Discrete Math. 345, No. 12, Article ID 113079, 10 p. (2022; Zbl 1497.05061) Full Text: DOI arXiv
Mynhardt, C. M.; Roux, A. Irredundance. (English) Zbl 1522.05356 Haynes, Teresa W. (ed.) et al., Structures of domination in graphs. Cham: Springer. Dev. Math. 66, 135-181 (2021). Reviewer: Venkatakrishnan Yanamandram (Tiruchirappalli) MSC: 05C69 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{A. Roux}, Dev. Math. 66, 135--181 (2021; Zbl 1522.05356) Full Text: DOI
Mynhardt, Christina M.; Raczek, Joanna Block graphs with large paired domination multisubdivision number. (English) Zbl 1458.05202 Discuss. Math., Graph Theory 41, No. 2, 665-684 (2021). MSC: 05C69 05C51 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{J. Raczek}, Discuss. Math., Graph Theory 41, No. 2, 665--684 (2021; Zbl 1458.05202) Full Text: DOI
Mynhardt, C. M.; Neilson, L. Comparing Upper Broadcast Domination and Boundary Independence Numbers of Graphs. arXiv:2104.02257 Preprint, arXiv:2104.02257 [math.CO] (2021). MSC: 05C69 BibTeX Cite \textit{C. M. Mynhardt} and \textit{L. Neilson}, ``Comparing Upper Broadcast Domination and Boundary Independence Numbers of Graphs'', Preprint, arXiv:2104.02257 [math.CO] (2021) Full Text: arXiv OA License
Mynhardt, C. M.; Wright, A. K. Constructing Triangle Decomposable Multigraphs with Minimum Multi-edges. arXiv:2108.07890 Preprint, arXiv:2108.07890 [math.CO] (2021). MSC: 05C70 05C10 BibTeX Cite \textit{C. M. Mynhardt} and \textit{A. K. Wright}, ``Constructing Triangle Decomposable Multigraphs with Minimum Multi-edges'', Preprint, arXiv:2108.07890 [math.CO] (2021) Full Text: arXiv OA License
Mynhardt, Kieka; Marchessault, Elise Lower Boundary Independent Broadcasts in Trees. arXiv:2105.04611 Preprint, arXiv:2105.04611 [math.CO] (2021). MSC: 05C69 BibTeX Cite \textit{K. Mynhardt} and \textit{E. Marchessault}, ``Lower Boundary Independent Broadcasts in Trees'', Preprint, arXiv:2105.04611 [math.CO] (2021) Full Text: arXiv OA License
Mynhardt, C. M.; Neilson, L. Lower Bound and Exact Values for the Boundary Independence Broadcast Number of a Tree. arXiv:2105.02312 Preprint, arXiv:2105.02312 [math.CO] (2021). MSC: 05C69 BibTeX Cite \textit{C. M. Mynhardt} and \textit{L. Neilson}, ``Lower Bound and Exact Values for the Boundary Independence Broadcast Number of a Tree'', Preprint, arXiv:2105.02312 [math.CO] (2021) Full Text: arXiv OA License
Mynhardt, C. M.; Neilson, L. A Sharp Upper Bound for the Boundary Independence Broadcast Number of a Tree. arXiv:2104.02266 Preprint, arXiv:2104.02266 [math.CO] (2021). MSC: 05C69 BibTeX Cite \textit{C. M. Mynhardt} and \textit{L. Neilson}, ``A Sharp Upper Bound for the Boundary Independence Broadcast Number of a Tree'', Preprint, arXiv:2104.02266 [math.CO] (2021) Full Text: arXiv OA License
Klostermeyer, William F.; Mynhardt, C. M. Eternal and secure domination in graphs. (English) Zbl 07445760 Haynes, Teresa W. (ed.) et al., Topics in domination in graphs. Cham: Springer. Dev. Math. 64, 445-478 (2020). MSC: 68-XX 05-XX PDFBibTeX XMLCite \textit{W. F. Klostermeyer} and \textit{C. M. Mynhardt}, Dev. Math. 64, 445--478 (2020; Zbl 07445760) Full Text: DOI
Mynhardt, Christina M.; Wodlinger, Jane L. The \(k\)-conversion number of regular graphs. (English) Zbl 1468.05295 AKCE Int. J. Graphs Comb. 17, No. 3, 955-965 (2020). MSC: 05C99 05C70 94C15 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{J. L. Wodlinger}, AKCE Int. J. Graphs Comb. 17, No. 3, 955--965 (2020; Zbl 1468.05295) Full Text: DOI arXiv
Mynhardt, C. M.; Neilson, L. Boundary independent broadcasts in graphs. (English) Zbl 1466.05168 J. Comb. Math. Comb. Comput. 116, 79-100 (2020). MSC: 05C69 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{L. Neilson}, J. Comb. Math. Comb. Comput. 116, 79--100 (2020; Zbl 1466.05168) Full Text: arXiv
Mynhardt, C. M.; Ogden, S. E. A. Total Roman domination edge-supercritical and edge-removal-supercritical graphs. (English) Zbl 1453.05092 Australas. J. Comb. 78, Part 3, 413-433 (2020). MSC: 05C69 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{S. E. A. Ogden}, Australas. J. Comb. 78, Part 3, 413--433 (2020; Zbl 1453.05092) Full Text: arXiv Link
Mynhardt, C. M.; Nasserasr, S. Reconfiguration of colourings and dominating sets in graphs. (English) Zbl 1451.05118 Chung, Fan (ed.) et al., 50 years of combinatorics, graph theory, and computing. Research surveys of the Southeastern international conference, SEICCGTC. Boca Raton, FL: CRC Press. Discrete Math. Appl. (Boca Raton), 171-191 (2020). MSC: 05C30 05C15 05C69 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{S. Nasserasr}, in: 50 years of combinatorics, graph theory, and computing. Research surveys of the Southeastern international conference, SEICCGTC. Boca Raton, FL: CRC Press. 171--191 (2020; Zbl 1451.05118)
Carr, MacKenzie; Mynhardt, Christina M.; Oellermann, Ortrud R. Enumerating the Digitally Convex Sets of Powers of Cycles and Cartesian Products of Paths and Complete Graphs. arXiv:2008.02781 Preprint, arXiv:2008.02781 [math.CO] (2020). MSC: 05C69 05C30 05C76 05C38 05A15 05A19 BibTeX Cite \textit{M. Carr} et al., ``Enumerating the Digitally Convex Sets of Powers of Cycles and Cartesian Products of Paths and Complete Graphs'', Preprint, arXiv:2008.02781 [math.CO] (2020) Full Text: arXiv OA License
Mynhardt, C. M.; Nasserasr, S. Reconfiguration of Colourings and Dominating Sets in Graphs: a Survey. arXiv:2003.05956 Preprint, arXiv:2003.05956 [math.CO] (2020). MSC: 05C15 05C69 BibTeX Cite \textit{C. M. Mynhardt} and \textit{S. Nasserasr}, ``Reconfiguration of Colourings and Dominating Sets in Graphs: a Survey'', Preprint, arXiv:2003.05956 [math.CO] (2020) Full Text: arXiv OA License
Mynhardt, Christina; Wodlinger, Jane A lower bound on the \(k\)-conversion number of graphs of maximum degree \(k+1\). (English) Zbl 1463.05412 Trans. Comb. 8, No. 3, 1-12 (2019). MSC: 05C69 PDFBibTeX XMLCite \textit{C. Mynhardt} and \textit{J. Wodlinger}, Trans. Comb. 8, No. 3, 1--12 (2019; Zbl 1463.05412) Full Text: DOI
Lampman, Chloe; Mynhardt, Kieka (C. M.); Ogden, Shannon Total Roman domination edge-critical graphs. (English) Zbl 1432.05072 Involve 12, No. 8, 1423-1439 (2019). MSC: 05C69 PDFBibTeX XMLCite \textit{C. Lampman} et al., Involve 12, No. 8, 1423--1439 (2019; Zbl 1432.05072) Full Text: DOI arXiv
Francis, M. D.; Mynhardt, C. M.; Wodlinger, Jane L. Subgraph-avoiding minimum decycling sets and \(k\)-conversion sets in graphs. (English) Zbl 1419.05072 Australas. J. Comb. 74, Part 2, 288-304 (2019). MSC: 05C15 PDFBibTeX XMLCite \textit{M. D. Francis} et al., Australas. J. Comb. 74, Part 2, 288--304 (2019; Zbl 1419.05072) Full Text: Link
Alikhani, S.; Fatehi, David; Mynhardt, C. M. On \(k\)-total dominating graphs. (English) Zbl 1411.05196 Australas. J. Comb. 73, Part 2, 313-333 (2019). MSC: 05C69 PDFBibTeX XMLCite \textit{S. Alikhani} et al., Australas. J. Comb. 73, Part 2, 313--333 (2019; Zbl 1411.05196) Full Text: arXiv Link
Mynhardt, C. M.; Teshima, L. E.; Roux, A. Connected \(k\)-dominating graphs. (English) Zbl 1400.05177 Discrete Math. 342, No. 1, 145-151 (2019). MSC: 05C69 PDFBibTeX XMLCite \textit{C. M. Mynhardt} et al., Discrete Math. 342, No. 1, 145--151 (2019; Zbl 1400.05177) Full Text: DOI arXiv
Mynhardt, C. M.; Teshima, L. E. A note on some variations of the \(\gamma\)-graph. (English) Zbl 1390.05173 J. Comb. Math. Comb. Comput. 104, 217-230 (2018). MSC: 05C69 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{L. E. Teshima}, J. Comb. Math. Comb. Comput. 104, 217--230 (2018; Zbl 1390.05173) Full Text: arXiv
Mynhardt, C. M.; Teshima, L. E. Broadcasts and multipackings in trees. (English) Zbl 1383.05242 Util. Math. 104, 227-242 (2017). MSC: 05C69 05C70 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{L. E. Teshima}, Util. Math. 104, 227--242 (2017; Zbl 1383.05242)
Gemmrich, L.; Mynhardt, C. M. Broadcasts in graphs: diametrical trees. (English) Zbl 1375.05195 Australas. J. Comb. 69, Part 2, 243-258 (2017). MSC: 05C69 05C12 05C05 PDFBibTeX XMLCite \textit{L. Gemmrich} and \textit{C. M. Mynhardt}, Australas. J. Comb. 69, Part 2, 243--258 (2017; Zbl 1375.05195) Full Text: arXiv Link
Boyer, Wanda; Macgillivray, Gary; Morrison, Laura; Mynhardt, Kieka; Nasserasr, Shahla Integer solutions to \(x^2+ y^2= z^2-k\) for a fixed integer value \(k\). (English) Zbl 1364.11077 Involve 10, No. 5, 881-892 (2017). MSC: 11D09 11A07 11A15 PDFBibTeX XMLCite \textit{W. Boyer} et al., Involve 10, No. 5, 881--892 (2017; Zbl 1364.11077) Full Text: DOI
Mynhardt, C. M.; Roux, A. Dominating and irredundant broadcasts in graphs. (English) Zbl 1355.05189 Discrete Appl. Math. 220, 80-90 (2017). MSC: 05C69 05C85 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{A. Roux}, Discrete Appl. Math. 220, 80--90 (2017; Zbl 1355.05189) Full Text: DOI arXiv
Klostermeyer, William F.; Mynhardt, C. M. Protecting a graph with mobile guards. (English) Zbl 1461.05157 Appl. Anal. Discrete Math. 10, No. 1, 1-29 (2016). MSC: 05C69 PDFBibTeX XMLCite \textit{W. F. Klostermeyer} and \textit{C. M. Mynhardt}, Appl. Anal. Discrete Math. 10, No. 1, 1--29 (2016; Zbl 1461.05157) Full Text: DOI arXiv
Mynhardt, Christina M.; van Bommel, Christopher M. Triangle decompositions of planar graphs. (English) Zbl 1339.05078 Discuss. Math., Graph Theory 36, No. 3, 643-659 (2016). MSC: 05C10 05C70 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{C. M. van Bommel}, Discuss. Math., Graph Theory 36, No. 3, 643--659 (2016; Zbl 1339.05078) Full Text: DOI arXiv
Klostermeyer, William; Mynhardt, Christina A dynamic domination problem in trees. (English) Zbl 1463.05406 Trans. Comb. 4, No. 4, 15-31 (2015). MSC: 05C69 05C05 PDFBibTeX XMLCite \textit{W. Klostermeyer} and \textit{C. Mynhardt}, Trans. Comb. 4, No. 4, 15--31 (2015; Zbl 1463.05406) Full Text: DOI
Mynhardt, C. M.; Wodlinger, J. Uniquely radial trees. (English) Zbl 1326.05109 J. Comb. Math. Comb. Comput. 93, 131-152 (2015). Reviewer: Sandi Klavžar (Ljubljana) MSC: 05C69 05C05 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{J. Wodlinger}, J. Comb. Math. Comb. Comput. 93, 131--152 (2015; Zbl 1326.05109)
Klostermeyer, William F.; Mynhardt, C. M. Domination, eternal domination, and clique covering. (English) Zbl 1311.05151 Discuss. Math., Graph Theory 35, No. 2, 283-300 (2015). MSC: 05C69 05C70 PDFBibTeX XMLCite \textit{W. F. Klostermeyer} and \textit{C. M. Mynhardt}, Discuss. Math., Graph Theory 35, No. 2, 283--300 (2015; Zbl 1311.05151) Full Text: DOI arXiv
Breytenbach, Jean A.; Mynhardt, C. M. Kieka On the \(\varepsilon\)-ascent chromatic index of complete graphs. (English) Zbl 1309.05067 Involve 8, No. 2, 295-305 (2015). MSC: 05C15 05C78 05C38 PDFBibTeX XMLCite \textit{J. A. Breytenbach} and \textit{C. M. Mynhardt}, Involve 8, No. 2, 295--305 (2015; Zbl 1309.05067) Full Text: DOI
Lunney, S.; Mynhardt, C. M. More trees with equal broadcast and domination numbers. (English) Zbl 1309.05139 Australas. J. Comb. 61, Part 3, 251-272 (2015). MSC: 05C69 PDFBibTeX XMLCite \textit{S. Lunney} and \textit{C. M. Mynhardt}, Australas. J. Comb. 61, Part 3, 251--272 (2015; Zbl 1309.05139) Full Text: Link
Kang, Jian; Mynhardt, C. M. Secure paired domination in graphs. (English) Zbl 1309.05135 AKCE Int. J. Graphs Comb. 11, No. 2, 177-197 (2014). Reviewer: Sandi Klavžar (Ljubljana) MSC: 05C69 PDFBibTeX XMLCite \textit{J. Kang} and \textit{C. M. Mynhardt}, AKCE Int. J. Graphs Comb. 11, No. 2, 177--197 (2014; Zbl 1309.05135)
Hartnell, B. L.; Mynhardt, C. M. On the difference between broadcast and multipacking numbers of graphs. (English) Zbl 1300.05224 Util. Math. 94, 19-29 (2014). MSC: 05C69 05C40 PDFBibTeX XMLCite \textit{B. L. Hartnell} and \textit{C. M. Mynhardt}, Util. Math. 94, 19--29 (2014; Zbl 1300.05224)
Hartnell, B. L.; Mynhardt, C. M. Independent protection in graphs. (English) Zbl 1298.05248 Discrete Math. 335, 100-109 (2014). MSC: 05C69 PDFBibTeX XMLCite \textit{B. L. Hartnell} and \textit{C. M. Mynhardt}, Discrete Math. 335, 100--109 (2014; Zbl 1298.05248) Full Text: DOI
Mynhardt, C. M.; Schurch, M. A construction of a class of graphs with depression three. (English) Zbl 1296.05087 Australas. J. Comb. 58, Part 2, 249-263 (2014). MSC: 05C22 05C38 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{M. Schurch}, Australas. J. Comb. 58, Part 2, 249--263 (2014; Zbl 1296.05087) Full Text: Link
Schurch, Mark; Mynhardt, Christine The depression of a graph and \(k\)-kernels. (English) Zbl 1290.05128 Discuss. Math., Graph Theory 34, No. 2, 233-247 (2014). MSC: 05C78 05C38 05C35 PDFBibTeX XMLCite \textit{M. Schurch} and \textit{C. Mynhardt}, Discuss. Math., Graph Theory 34, No. 2, 233--247 (2014; Zbl 1290.05128) Full Text: DOI
Mynhardt, C. M.; Schurch, M. A class of graphs with depression three. (English) Zbl 1277.05083 Discrete Math. 313, No. 11, 1224-1232 (2013). MSC: 05C30 05C38 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{M. Schurch}, Discrete Math. 313, No. 11, 1224--1232 (2013; Zbl 1277.05083) Full Text: DOI
Goldwasser, John L.; Klostermeyer, William F.; Mynhardt, C. M. Eternal protection in grid graphs. (English) Zbl 1300.05177 Util. Math. 91, 47-64 (2013). Reviewer: Markus Fulmek (Wien) MSC: 05C57 91A43 05C30 05C69 PDFBibTeX XMLCite \textit{J. L. Goldwasser} et al., Util. Math. 91, 47--64 (2013; Zbl 1300.05177)
Mynhardt, C. M.; Wodlinger, J. A class of trees with equal broadcast and domination numbers. (English) Zbl 1276.05029 Australas. J. Comb. 56, 3-22 (2013). Reviewer: Hans Peter Künzi (Rondebosch) MSC: 05C05 05C69 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{J. Wodlinger}, Australas. J. Comb. 56, 3--22 (2013; Zbl 1276.05029)
Brewster, Richard C.; Mynhardt, Christina M.; Teshima, Laura E. New bounds for the broadcast domination number of a graph. (English) Zbl 1266.05109 Cent. Eur. J. Math. 11, No. 7, 1334-1343 (2013). MSC: 05C69 05C70 PDFBibTeX XMLCite \textit{R. C. Brewster} et al., Cent. Eur. J. Math. 11, No. 7, 1334--1343 (2013; Zbl 1266.05109) Full Text: DOI
Klostermeyer, William F.; Mynhardt, Christina M. Eternal total domination in graphs. (English) Zbl 1289.05351 Ars Comb. 107, 473-492 (2012). Reviewer: Herbert Fleischner (Wien) MSC: 05C69 PDFBibTeX XMLCite \textit{W. F. Klostermeyer} and \textit{C. M. Mynhardt}, Ars Comb. 107, 473--492 (2012; Zbl 1289.05351)
Benecke, Stephen; Mynhardt, Christina M. Characterizing Cartesian fixers and multipliers. (English) Zbl 1255.05163 Discuss. Math., Graph Theory 32, No. 1, 161-175 (2012). MSC: 05C76 05C69 05C99 PDFBibTeX XMLCite \textit{S. Benecke} and \textit{C. M. Mynhardt}, Discuss. Math., Graph Theory 32, No. 1, 161--175 (2012; Zbl 1255.05163) Full Text: DOI Link
Targhi, E. Ebrahimi; Rad, N. Jafari; Mynhardt, C. M.; Wu, Y. Bounds for independent Roman domination in graphs. (English) Zbl 1247.05154 J. Comb. Math. Comb. Comput. 80, 351-365 (2012). MSC: 05C60 PDFBibTeX XMLCite \textit{E. E. Targhi} et al., J. Comb. Math. Comb. Comput. 80, 351--365 (2012; Zbl 1247.05154)
Klostermeyer, William F.; Mynhardt, C. M. Vertex covers and eternal dominating sets. (English) Zbl 1408.05099 Discrete Appl. Math. 160, No. 7-8, 1183-1190 (2012). MSC: 05C69 05C70 PDFBibTeX XMLCite \textit{W. F. Klostermeyer} and \textit{C. M. Mynhardt}, Discrete Appl. Math. 160, No. 7--8, 1183--1190 (2012; Zbl 1408.05099) Full Text: DOI
Mynhardt, Christina M.; Schurch, Mark Paired domination in prisms of graphs. (English) Zbl 1238.05201 Discuss. Math., Graph Theory 31, No. 1, 5-23 (2011). MSC: 05C69 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{M. Schurch}, Discuss. Math., Graph Theory 31, No. 1, 5--23 (2011; Zbl 1238.05201) Full Text: DOI
Klostermeyer, William F.; Mynhardt, C. M. Graphs with equal eternal vertex cover and eternal domination numbers. (English) Zbl 1223.05232 Discrete Math. 311, No. 14, 1371-1379 (2011). MSC: 05C70 05C69 PDFBibTeX XMLCite \textit{W. F. Klostermeyer} and \textit{C. M. Mynhardt}, Discrete Math. 311, No. 14, 1371--1379 (2011; Zbl 1223.05232) Full Text: DOI
Cockayne, E. J.; Herke, S.; Mynhardt, C. M. Broadcasts and domination in trees. (English) Zbl 1222.05196 Discrete Math. 311, No. 13, 1235-1246 (2011). MSC: 05C69 05C05 PDFBibTeX XMLCite \textit{E. J. Cockayne} et al., Discrete Math. 311, No. 13, 1235--1246 (2011; Zbl 1222.05196) Full Text: DOI
Benecke, S.; Mynhardt, C. M. A domination algorithm for generalized Cartesian products. (English) Zbl 1232.05156 J. Comb. Math. Comb. Comput. 75, 65-84 (2010). MSC: 05C69 05C99 05C85 05C76 PDFBibTeX XMLCite \textit{S. Benecke} and \textit{C. M. Mynhardt}, J. Comb. Math. Comb. Comput. 75, 65--84 (2010; Zbl 1232.05156)
Edwards, M.; Mynhardt, C. M. Acyclic orientations and monotonicity in graphs. (English) Zbl 1198.05077 J. Comb. Math. Comb. Comput. 73, 15-29 (2010). MSC: 05C20 05C38 PDFBibTeX XMLCite \textit{M. Edwards} and \textit{C. M. Mynhardt}, J. Comb. Math. Comb. Comput. 73, 15--29 (2010; Zbl 1198.05077)
Benecke, S.; Mynhardt, C. M. Domination of generalized Cartesian products. (English) Zbl 1201.05069 Discrete Math. 310, No. 8, 1392-1397 (2010). MSC: 05C69 05C76 PDFBibTeX XMLCite \textit{S. Benecke} and \textit{C. M. Mynhardt}, Discrete Math. 310, No. 8, 1392--1397 (2010; Zbl 1201.05069) Full Text: DOI
Burger, A. P.; Mynhardt, C. M. Regular graphs are not universal fixers. (English) Zbl 1216.05098 Discrete Math. 310, No. 2, 364-368 (2010). MSC: 05C69 05C25 05A05 PDFBibTeX XMLCite \textit{A. P. Burger} and \textit{C. M. Mynhardt}, Discrete Math. 310, No. 2, 364--368 (2010; Zbl 1216.05098) Full Text: DOI
Klostermeyer, William F.; Mynhardt, C. M. Edge protection in graphs. (English) Zbl 1207.05141 Australas. J. Comb. 45, 235-250 (2009). MSC: 05C69 PDFBibTeX XMLCite \textit{W. F. Klostermeyer} and \textit{C. M. Mynhardt}, Australas. J. Comb. 45, 235--250 (2009; Zbl 1207.05141)
Grobler, P. J. P.; Mynhardt, C. M. Secure domination critical graphs. (English) Zbl 1189.05126 Discrete Math. 309, No. 19, 5820-5827 (2009). MSC: 05C69 05C35 PDFBibTeX XMLCite \textit{P. J. P. Grobler} and \textit{C. M. Mynhardt}, Discrete Math. 309, No. 19, 5820--5827 (2009; Zbl 1189.05126) Full Text: DOI
Herke, S.; Mynhardt, C. M. Radial trees. (English) Zbl 1221.05051 Discrete Math. 309, No. 20, 5950-5962 (2009). MSC: 05C05 05C12 05C85 PDFBibTeX XMLCite \textit{S. Herke} and \textit{C. M. Mynhardt}, Discrete Math. 309, No. 20, 5950--5962 (2009; Zbl 1221.05051) Full Text: DOI
Mynhardt, C. M.; Xu, Zhixia Domination in prisms of graphs: universal fixers. (English) Zbl 1284.05199 Util. Math. 78, 185-201 (2009). MSC: 05C69 PDFBibTeX XMLCite \textit{C. M. Mynhardt} and \textit{Z. Xu}, Util. Math. 78, 185--201 (2009; Zbl 1284.05199)
Cockayne, E. J.; Gibson, R. G.; Mynhardt, C. M. Claw-free graphs are not universal fixers. (English) Zbl 1219.05116 Discrete Math. 309, No. 1, 128-133 (2009). MSC: 05C69 PDFBibTeX XMLCite \textit{E. J. Cockayne} et al., Discrete Math. 309, No. 1, 128--133 (2009; Zbl 1219.05116) Full Text: DOI
Henning, Michael A.; Mynhardt, Christina M. The diameter of paired-domination vertex critical graphs. (English) Zbl 1174.05093 Czech. Math. J. 58, No. 4, 887-897 (2008). MSC: 05C69 05C35 PDFBibTeX XMLCite \textit{M. A. Henning} and \textit{C. M. Mynhardt}, Czech. Math. J. 58, No. 4, 887--897 (2008; Zbl 1174.05093) Full Text: DOI EuDML Link
Bullock, Frank; Frick, Marietjie; Singleton, Joy; van Aardt, Susan; Mynhardt, Kieka (C. M.) Maximal nontraceable graphs with toughness less than one. (English) Zbl 1180.05056 Electron. J. Comb. 15, No. 1, Research Paper R18, 19 p. (2008). MSC: 05C38 05C45 PDFBibTeX XMLCite \textit{F. Bullock} et al., Electron. J. Comb. 15, No. 1, Research Paper R18, 19 p. (2008; Zbl 1180.05056) Full Text: EuDML EMIS
Klostermeyer, William F.; Mynhardt, Christina M. Secure domination and secure total domination in graphs. (English) Zbl 1156.05043 Discuss. Math., Graph Theory 28, No. 2, 267-284 (2008). MSC: 05C69 PDFBibTeX XMLCite \textit{W. F. Klostermeyer} and \textit{C. M. Mynhardt}, Discuss. Math., Graph Theory 28, No. 2, 267--284 (2008; Zbl 1156.05043) Full Text: DOI
Cockayne, E. J.; Favaron, O.; Finbow, S.; Mynhardt, C. M. Open irredundance and maximum degree in graphs. (English) Zbl 1207.05095 Discrete Math. 308, No. 23, 5358-5375 (2008). MSC: 05C35 05C69 PDFBibTeX XMLCite \textit{E. J. Cockayne} et al., Discrete Math. 308, No. 23, 5358--5375 (2008; Zbl 1207.05095) Full Text: DOI
Benecke, S.; Mynhardt, C. M. Trees with domination subdivision number one. (English) Zbl 1153.05018 Australas. J. Comb. 42, 201-209 (2008). MSC: 05C05 05C69 05C35 05C85 PDFBibTeX XMLCite \textit{S. Benecke} and \textit{C. M. Mynhardt}, Australas. J. Comb. 42, 201--209 (2008; Zbl 1153.05018)
Frick, Marietjie; Fricke, Gerd H.; Mynhardt, Christina M.; Skaggs, R. Duane Critical graphs with respect to vertex identification. (English) Zbl 1170.05035 Util. Math. 76, 213-227 (2008). MSC: 05C35 05C69 PDFBibTeX XMLCite \textit{M. Frick} et al., Util. Math. 76, 213--227 (2008; Zbl 1170.05035)
Edwards, M.; Gibson, R. G.; Henning, M. A.; Mynhardt, C. M. Diameter of paired domination edge-critical graphs. (English) Zbl 1169.05032 Australas. J. Comb. 40, 279-291 (2008). MSC: 05C69 PDFBibTeX XMLCite \textit{M. Edwards} et al., Australas. J. Comb. 40, 279--291 (2008; Zbl 1169.05032)
Mynhardt, C. M. Trees with depression three. (English) Zbl 1149.05042 Discrete Math. 308, No. 5-6, 855-864 (2008). Reviewer: László A. Székely (Columbia) MSC: 05C78 05C38 05C05 PDFBibTeX XMLCite \textit{C. M. Mynhardt}, Discrete Math. 308, No. 5--6, 855--864 (2008; Zbl 1149.05042) Full Text: DOI
Benecke, S.; Cockayne, E. J.; Mynhardt, C. M. Secure total domination in graphs. (English) Zbl 1183.05055 Util. Math. 74, 247-259 (2007). MSC: 05C69 PDFBibTeX XMLCite \textit{S. Benecke} et al., Util. Math. 74, 247--259 (2007; Zbl 1183.05055)
Gibson, Richard G.; Mynhardt, Christina M. Counterexample to a conjecture on the structure of bipartite partitionable graphs. (English) Zbl 1142.05059 Discuss. Math., Graph Theory 27, No. 3, 527-540 (2007). MSC: 05C69 PDFBibTeX XMLCite \textit{R. G. Gibson} and \textit{C. M. Mynhardt}, Discuss. Math., Graph Theory 27, No. 3, 527--540 (2007; Zbl 1142.05059) Full Text: DOI
Dorfling, Michael; Goddard, Wayne; Henning, Michael A.; Mynhardt, C. M. Construction of trees and graphs with equal domination parameters. (English) Zbl 1104.05053 Discrete Math. 306, No. 21, 2647-2654 (2006). MSC: 05C69 PDFBibTeX XMLCite \textit{M. Dorfling} et al., Discrete Math. 306, No. 21, 2647--2654 (2006; Zbl 1104.05053) Full Text: DOI
Cockayne, E. J.; Geldenhuys, G.; Grobler, P. J. P.; Mynhardt, C. M.; van Vuuren, J. H. The depression of a graph. (English) Zbl 1111.05086 Util. Math. 69, 143-160 (2006). Reviewer: Gabriel Semanišin (Košice) MSC: 05C78 05C75 05C38 PDFBibTeX XMLCite \textit{E. J. Cockayne} et al., Util. Math. 69, 143--160 (2006; Zbl 1111.05086)
Cockayne, E. J.; Mynhardt, C. M. A lower bound for the depression of trees. (English) Zbl 1094.05018 Australas. J. Comb. 35, 319-328 (2006). Reviewer: László A. Székely (Columbia) MSC: 05C05 05C35 PDFBibTeX XMLCite \textit{E. J. Cockayne} and \textit{C. M. Mynhardt}, Australas. J. Comb. 35, 319--328 (2006; Zbl 1094.05018)
Mynhardt, C. M.; Swart, H. C.; Ungerer, E. Excellent trees and secure domination. (English) Zbl 1071.05058 Util. Math. 67, 255-267 (2005). Reviewer: Peter Horák (Tacoma) MSC: 05C69 PDFBibTeX XMLCite \textit{C. M. Mynhardt} et al., Util. Math. 67, 255--267 (2005; Zbl 1071.05058)
Haynes, T. W.; Mynhardt, C. M.; van der Merwe, L. C. Realizability of the total domination criticality index. (English) Zbl 1103.05061 Util. Math. 67, 3-8 (2005). Reviewer: Bert Randerath (Köln) MSC: 05C69 PDFBibTeX XMLCite \textit{T. W. Haynes} et al., Util. Math. 67, 3--8 (2005; Zbl 1103.05061)
Mynhardt, C. M.; Burger, A. P.; Clark, T. C.; Falvai, B.; Henderson, N. D. R. Altitude of regular graphs with girth at least five. (English) Zbl 1062.05131 Discrete Math. 294, No. 3, 241-257 (2005). MSC: 05C78 05C15 05C38 PDFBibTeX XMLCite \textit{C. M. Mynhardt} et al., Discrete Math. 294, No. 3, 241--257 (2005; Zbl 1062.05131) Full Text: DOI
Cochayne, E. J.; Mynhardt, C. M. Altitude of \(K_{3,n}\). (English) Zbl 1073.05062 J. Comb. Math. Comb. Comput. 52, 143-157 (2005). Reviewer: Hans L. Bodlaender (Utrecht) MSC: 05C78 05C38 PDFBibTeX XMLCite \textit{E. J. Cochayne} and \textit{C. M. Mynhardt}, J. Comb. Math. Comb. Comput. 52, 143--157 (2005; Zbl 1073.05062)
Burger, A. P.; Cockayne, E. J.; Mynhardt, C. M. Altitude of small complete and complete bipartite graphs. (English) Zbl 1080.05046 Australas. J. Comb. 31, 167-177 (2005). Reviewer: Lai Chunhui (Zhangzhou) MSC: 05C38 05C35 PDFBibTeX XMLCite \textit{A. P. Burger} et al., Australas. J. Comb. 31, 167--177 (2005; Zbl 1080.05046)
Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. Total domination in \(K_ r\)-covered graphs. (English) Zbl 1078.05063 Ars Comb. 71, 289-303 (2004). Reviewer: Ko-Wei Lih (Nankang) MSC: 05C69 PDFBibTeX XMLCite \textit{E. J. Cockayne} et al., Ars Comb. 71, 289--303 (2004; Zbl 1078.05063)
Clark, T. C.; Falvai, B.; Hendersonand, D. R.; Mynhardt, C. M. Altitude of 4-regular circulants. (English) Zbl 1073.05061 AKCE Int. J. Graphs Comb. 1, No. 2, 149-166 (2004). Reviewer: Clemens Heuberger (Graz) MSC: 05C78 05C15 05C38 PDFBibTeX XMLCite \textit{T. C. Clark} et al., AKCE Int. J. Graphs Comb. 1, No. 2, 149--166 (2004; Zbl 1073.05061)
Burger, Alewyn; Mynhardt, Christina M.; Weakley, William D. On the domination number of prisms of graphs. (English) Zbl 1064.05111 Discuss. Math., Graph Theory 24, No. 2, 303-318 (2004). MSC: 05C69 PDFBibTeX XMLCite \textit{A. Burger} et al., Discuss. Math., Graph Theory 24, No. 2, 303--318 (2004; Zbl 1064.05111) Full Text: DOI Link
Burger, A. P.; Cockayne, E. J.; Gründlingh, W. R.; Mynhardt, C. M.; van Vuuren, J. H.; Winterbach, W. Finite order domination in graphs. (English) Zbl 1052.05053 J. Comb. Math. Comb. Comput. 49, 159-175 (2004). Reviewer: William G. Brown (Montréal) MSC: 05C69 PDFBibTeX XMLCite \textit{A. P. Burger} et al., J. Comb. Math. Comb. Comput. 49, 159--175 (2004; Zbl 1052.05053)
Burger, A. P.; Mynhardt, C. M.; Cockayne, E. J. Regular solutions of the \(n\)-queens problem on the torus. (English) Zbl 1052.05057 Util. Math. 65, 219-230 (2004). Reviewer: Bohdan Zelinka (Liberec) MSC: 05C70 05C69 11B75 PDFBibTeX XMLCite \textit{A. P. Burger} et al., Util. Math. 65, 219--230 (2004; Zbl 1052.05057)
Burger, A. P.; Cockayne, E. J.; Gründlingh, W. R.; Mynhardt, C. M.; van Vuuren, J. H.; Winterbach, W. Infinite order domination in graphs. (English) Zbl 1052.05054 J. Comb. Math. Comb. Comput. 50, 179-194 (2004). Reviewer: William G. Brown (Montréal) MSC: 05C69 PDFBibTeX XMLCite \textit{A. P. Burger} et al., J. Comb. Math. Comb. Comput. 50, 179--194 (2004; Zbl 1052.05054)
Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. On \(i^{-}\)-ER-critical graphs. (English) Zbl 1031.05093 Discrete Math. 276, No. 1-3, 111-125 (2004). MSC: 05C69 PDFBibTeX XMLCite \textit{E. J. Cockayne} et al., Discrete Math. 276, No. 1--3, 111--125 (2004; Zbl 1031.05093) Full Text: DOI
van der Merwe, L. C.; Mynhardt, C. M.; Haynes, T. W. Total domination edge critical graphs with minimum diameter. (English) Zbl 1072.05557 Ars Comb. 66, 79-96 (2003). Reviewer: Bohdan Zelinka (Liberec) MSC: 05C69 PDFBibTeX XMLCite \textit{L. C. van der Merwe} et al., Ars Comb. 66, 79--96 (2003; Zbl 1072.05557)
Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. Secure domination, weak Roman domination and forbidden subgraphs. (English) Zbl 1051.05065 Bull. Inst. Comb. Appl. 39, 87-100 (2003). Reviewer: Ortrud R. Oellermann (Winnipeg) MSC: 05C69 PDFBibTeX XMLCite \textit{E. J. Cockayne} et al., Bull. Inst. Comb. Appl. 39, 87--100 (2003; Zbl 1051.05065)
Mynhardt, Christina M. Upper bounds for the domination numbers of toroidal queens graphs. (English) Zbl 1035.05066 Discuss. Math., Graph Theory 23, No. 1, 163-175 (2003). Reviewer: Ioan Tomescu (Bucureşti) MSC: 05C69 PDFBibTeX XMLCite \textit{C. M. Mynhardt}, Discuss. Math., Graph Theory 23, No. 1, 163--175 (2003; Zbl 1035.05066) Full Text: DOI Link
Burger, A. P.; Mynhardt, C. M.; Weakley, William D. The domination number of the toroidal queens graph of size \(3k\times 3k\). (English) Zbl 1030.05094 Australas. J. Comb. 28, 137-148 (2003). Reviewer: Gregory Gutin (Egham) MSC: 05C69 PDFBibTeX XMLCite \textit{A. P. Burger} et al., Australas. J. Comb. 28, 137--148 (2003; Zbl 1030.05094)
Cockayne, E. J.; Favaron, O.; Goddard, W.; Grobler, P. J. P.; Mynhardt, C. M. Changing upper irredundance by edge addition. (English) Zbl 1023.05106 Discrete Math. 266, No. 1-3, 185-193 (2003). Reviewer: Gregory Gutin (Egham) MSC: 05C69 PDFBibTeX XMLCite \textit{E. J. Cockayne} et al., Discrete Math. 266, No. 1--3, 185--193 (2003; Zbl 1023.05106) Full Text: DOI
Burger, A. P.; Mynhardt, C. M. An improved upper bound for queens domination numbers. (English) Zbl 1015.05066 Discrete Math. 266, No. 1-3, 119-131 (2003). Reviewer: Patric R.J.Östergård (Helsinki) MSC: 05C69 PDFBibTeX XMLCite \textit{A. P. Burger} and \textit{C. M. Mynhardt}, Discrete Math. 266, No. 1--3, 119--131 (2003; Zbl 1015.05066) Full Text: DOI
Cockayne, Ernest J.; Henning, Michael A.; Mynhardt, Christina M. Vertices contained in all or in no minimum total dominating set of a tree. (English) Zbl 1013.05054 Discrete Math. 260, No. 1-3, 37-44 (2003). Reviewer: William G.Brown (Montréal) MSC: 05C69 05C05 PDFBibTeX XMLCite \textit{E. J. Cockayne} et al., Discrete Math. 260, No. 1--3, 37--44 (2003; Zbl 1013.05054) Full Text: DOI
Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. Total domination in claw-free cubic graphs. (English) Zbl 1011.05043 J. Comb. Math. Comb. Comput. 43, 219-225 (2002). Reviewer: Ekkehard Köhler (Berlin) MSC: 05C69 05C35 PDFBibTeX XMLCite \textit{E. J. Cockayne} et al., J. Comb. Math. Comb. Comput. 43, 219--225 (2002; Zbl 1011.05043)
Burger, A. P.; Mynhardt, C. M. An upper bound for the minimum number of queens covering the \(n {\times} n\) chessboard. (English) Zbl 0993.05105 Discrete Appl. Math. 121, No. 1-3, 51-60 (2002). Reviewer: Dieter Rautenbach (Aachen) MSC: 05C69 PDFBibTeX XMLCite \textit{A. P. Burger} and \textit{C. M. Mynhardt}, Discrete Appl. Math. 121, No. 1--3, 51--60 (2002; Zbl 0993.05105) Full Text: DOI
Cockayne, E. J.; Favaron, O.; Grobler, P. J. P.; Mynhardt, C. M.; Puech, J. Generalised Ramsey numbers with respect to classes of graphs. (English) Zbl 1066.05094 Ars Comb. 59, 279-288 (2001). Reviewer: Bohdan Zelinka (Liberec) MSC: 05C55 PDFBibTeX XMLCite \textit{E. J. Cockayne} et al., Ars Comb. 59, 279--288 (2001; Zbl 1066.05094)
van der Merwe, Lucas C.; Mynhardt, Cristine M.; Haynes, Theresa W. Total domination edge critical graphs with maximum diameter. (English) Zbl 1007.05077 Discuss. Math., Graph Theory 21, No. 2, 187-205 (2001). Reviewer: Herman J.Servatius (Worcester) MSC: 05C69 PDFBibTeX XMLCite \textit{L. C. van der Merwe} et al., Discuss. Math., Graph Theory 21, No. 2, 187--205 (2001; Zbl 1007.05077) Full Text: DOI