Edit Profile (opens in new tab) Mynhardt, Christina Magdalena Co-Author Distance Author ID: mynhardt.christina-m Published as: Mynhardt, C. M.; Mynhardt, Christina M.; Mynhardt, Christine; Mynhardt, Kieka; Mynhardt, Kieka (C. M.); Mynhardt, Christina; Mynhardt, C. M. Kieka; Mynhardt, Cristine M.; Mynhart, Christina M. more...less External Links: MGP · Wikidata · dblp Documents Indexed: 187 Publications since 1979, including 11 Additional arXiv Preprints Co-Authors: 79 Co-Authors with 169 Joint Publications 1,518 Co-Co-Authors all top 5 Co-Authors 11 single-authored 69 Cockayne, Ernest J. 17 Burger, Alewyn Petrus 17 Favaron, Odile 10 Klostermeyer, William F. 9 Grobler, P. J. P. 8 MacGillivray, Gary 7 Brewster, Richard C. 7 Teshima, Laura E. 6 Haynes, Teresa W. 6 Puech, Joël 6 van der Merwe, Lucas C. 5 Benecke, Stephen 5 Broere, Izak 5 Chartrand, Gary Theodore 5 Henning, Michael Anthony 5 Neilson, Linda 5 Saba, Farrokh 5 Wodlinger, Jane L. 4 Schurch, Mark 3 Fricke, Gerd H. 3 Gibson, Richard G. jun. 3 Goddard, Wayne Dean 3 Hattingh, Johannes H. 3 Nasserasr, Shahla 3 van Vuuren, Jan Harm 2 Clark, T. C. 2 Falvai, B. 2 Frick, Marietjie 2 Gründlingh, W. R. 2 Hartnell, Bert L. 2 Hedetniemi, Stephen Travis 2 Oellermann, Ortrud R. 2 Weakley, William D. 2 Winterbach, W. 2 Yu, Bo 1 Alikhani, Saeid 1 Ao, Shengmei 1 Bollobás, Béla 1 Boyer, Wanda 1 Breytenbach, Jean A. 1 Bullock, Frank 1 Carr, MacKenzie 1 Cochayne, E. J. 1 Dorfling, Michael J. 1 Ebrahimi Targhi, E. 1 Fatehi, David 1 Finbow, Stephen 1 Francis, Michael D. 1 Geldenhuys, Gerhard 1 Gemmrich, L. 1 Goldwasser, John L. 1 Hedetniemi, Sandra Lee Mitchell 1 Henderson, N. D. R. 1 Hendersonand, D. R. 1 Hoepner, Jules 1 Jafari Rad, Nader 1 Kang, Jian 1 Kubicki, Grzegorz M. 1 Lampman, Chloe 1 Lesniak, Linda M. 1 Lorimer, Peter 1 Lunney, S. 1 Marchessault, Elise 1 McCrea, Devon 1 McGillivray, Gary 1 Morrison, Laura 1 Ogden, S. E. A. 1 Ogden, Shannon 1 Raczek, Joanna 1 Singleton, Joy Elizabeth 1 Skaggs, R. Duane 1 Swart, Henda C. 1 Ungerer, Elna 1 van Aardt, Susan A. 1 van Bommel, Christopher M. 1 Virgile, Virgélot 1 Wright, Andrew K. 1 Wu, Yunjian 1 Xu, Zhixia all top 5 Serials 34 Discrete Mathematics 21 Utilitas Mathematica 19 JCMCC. The Journal of Combinatorial Mathematics and Combinatorial Computing 16 The Australasian Journal of Combinatorics 14 Ars Combinatoria 13 Discussiones Mathematicae. Graph Theory 12 Journal of Graph Theory 6 Bulletin of the Institute of Combinatorics and its Applications 5 Quaestiones Mathematicae 4 Discrete Applied Mathematics 3 Congressus Numerantium 3 AKCE International Journal of Graphs and Combinatorics 3 Involve 3 Transactions on Combinatorics 1 Czechoslovak Mathematical Journal 1 Networks 1 Graphs and Combinatorics 1 Combinatorics, Probability and Computing 1 The Electronic Journal of Combinatorics 1 Central European Journal of Mathematics 1 Applicable Analysis and Discrete Mathematics 1 Electronic Journal of Graph Theory and Applications all top 5 Fields 184 Combinatorics (05-XX) 2 Number theory (11-XX) 2 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Computer science (68-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 145 Publications have been cited 1,027 times in 486 Documents Cited by ▼ Year ▼ Total domination edge critical graphs. Zbl 0918.05069 van der Merwe, L. C.; Mynhardt, C. M.; Haynes, T. W. 40 1998 Infinite order domination in graphs. Zbl 1052.05054 Burger, A. P.; Cockayne, E. J.; Gründlingh, W. R.; Mynhardt, C. M.; van Vuuren, J. H.; Winterbach, W. 39 2004 Secure domination, weak Roman domination and forbidden subgraphs. Zbl 1051.05065 Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. 37 2003 Secure domination and secure total domination in graphs. Zbl 1156.05043 Klostermeyer, William F.; Mynhardt, Christina M. 32 2008 Protecting a graph with mobile guards. Zbl 1461.05157 Klostermeyer, William F.; Mynhardt, C. M. 28 2016 Construction of trees and graphs with equal domination parameters. Zbl 1104.05053 Dorfling, Michael; Goddard, Wayne; Henning, Michael A.; Mynhardt, C. M. 26 2006 On a generalization of signed dominating functions of graphs. Zbl 0881.05060 Cockayne, E. J.; Mynhardt, C. M. 25 1996 Total domination in graphs with minimum degree three. Zbl 0945.05047 Favaron, Odile; Henning, Michael A.; Mynhart, Christina M.; Puech, Joël 24 2000 Generalized colorings of outerplanar and planar graphs. Zbl 0571.05017 Broere, I.; Mynhardt, C. M. 24 1985 Reinforcement in graphs. Zbl 0862.05071 Kok, J.; Mynhardt, C. M. 23 1990 Excellent trees and secure domination. Zbl 1071.05058 Mynhardt, C. M.; Swart, H. C.; Ungerer, E. 22 2005 Vertices contained in every minimum dominating set of a tree. Zbl 0931.05063 Mynhardt, C. M. 21 1999 Finite order domination in graphs. Zbl 1052.05053 Burger, A. P.; Cockayne, E. J.; Gründlingh, W. R.; Mynhardt, C. M.; van Vuuren, J. H.; Winterbach, W. 21 2004 Radial trees. Zbl 1221.05051 Herke, S.; Mynhardt, C. M. 17 2009 Broadcasts and multipackings in trees. Zbl 1383.05242 Mynhardt, C. M.; Teshima, L. E. 17 2017 Total domination edge critical graphs with maximum diameter. Zbl 1007.05077 van der Merwe, Lucas C.; Mynhardt, Cristine M.; Haynes, Theresa W. 16 2001 Reconfiguration of colourings and dominating sets in graphs. Zbl 1451.05118 Mynhardt, C. M.; Nasserasr, S. 16 2020 Secure domination critical graphs. Zbl 1189.05126 Grobler, P. J. P.; Mynhardt, C. M. 15 2009 Graphs with equal eternal vertex cover and eternal domination numbers. Zbl 1223.05232 Klostermeyer, William F.; Mynhardt, C. M. 14 2011 Secure total domination in graphs. Zbl 1183.05055 Benecke, S.; Cockayne, E. J.; Mynhardt, C. M. 14 2007 Edge protection in graphs. Zbl 1207.05141 Klostermeyer, William F.; Mynhardt, C. M. 14 2009 Criticality index of total domination. Zbl 0951.05081 van der Merwe, Lucas C.; Mynhardt, Christina M.; Haynes, Teresa W. 13 1998 Total domination edge critical graphs with minimum diameter. Zbl 1072.05557 van der Merwe, L. C.; Mynhardt, C. M.; Haynes, T. W. 13 2003 The sequence of upper and lower domination, independence and irredundance numbers of a graph. Zbl 0788.05055 Cockayne, E. J.; Mynhardt, C. M. 13 1993 New bounds for the broadcast domination number of a graph. Zbl 1266.05109 Brewster, Richard C.; Mynhardt, Christina M.; Teshima, Laura E. 13 2013 Eternal protection in grid graphs. Zbl 1300.05177 Goldwasser, John L.; Klostermeyer, William F.; Mynhardt, C. M. 13 2013 On the product of upper irredundance numbers of a graph and its complement. Zbl 0672.05049 Cockayne, E. J.; Mynhardt, C. M. 12 1989 A characterization of \((\gamma,i)\)-trees. Zbl 0949.05059 Cockayne, E. J.; Favaron, O.; Mynhardt, C. M.; Puech, J. 12 2000 3-domination critical graphs with arbitrary independent domination numbers. Zbl 0944.05074 van der Merwe, L. C.; Mynhardt, C. M.; Haynes, T. W. 11 1999 Vertices contained in all or in no minimum total dominating set of a tree. Zbl 1013.05054 Cockayne, Ernest J.; Henning, Michael A.; Mynhardt, Christina M. 11 2003 Irredundance and maximum degree in graphs. Zbl 0881.05068 Cockayne, E. J.; Mynhardt, C. M. 11 1997 Broadcasts and domination in trees. Zbl 1222.05196 Cockayne, E. J.; Herke, S.; Mynhardt, C. M. 11 2011 On a Nordhaus-Gaddum type problem for independent domination. Zbl 0820.05039 Cockayne, E. J.; Fricke, G.; Mynhardt, C. M. 9 1995 Vertex covers and eternal dominating sets. Zbl 1408.05099 Klostermeyer, William F.; Mynhardt, C. M. 9 2012 The diameter of paired-domination vertex critical graphs. Zbl 1174.05093 Henning, Michael A.; Mynhardt, Christina M. 9 2008 On the domination number of prisms of graphs. Zbl 1064.05111 Burger, Alewyn; Mynhardt, Christina M.; Weakley, William D. 9 2004 Connected \(k\)-dominating graphs. Zbl 1400.05177 Mynhardt, C. M.; Teshima, L. E.; Roux, A. 9 2019 Altitude of small complete and complete bipartite graphs. Zbl 1080.05046 Burger, A. P.; Cockayne, E. J.; Mynhardt, C. M. 8 2005 Altitude of regular graphs with girth at least five. Zbl 1062.05131 Mynhardt, C. M.; Burger, A. P.; Clark, T. C.; Falvai, B.; Henderson, N. D. R. 8 2005 On the difference between broadcast and multipacking numbers of graphs. Zbl 1300.05224 Hartnell, B. L.; Mynhardt, C. M. 8 2014 A note on some variations of the \(\gamma\)-graph. Zbl 1390.05173 Mynhardt, C. M.; Teshima, L. E. 8 2018 Properties of minimal dominating functions of graphs. Zbl 0840.05090 Cockayne, E. J.; Fricke, G.; Hedetniemi, S. T.; Mynhardt, C. M. 7 1995 Domination critical graphs with higher independent domination numbers. Zbl 0852.05053 Ao, S.; Cockayne, E. J.; MacGillivray, G.; Mynhardt, C. M. 7 1996 Total dominating functions in trees: Minimality and convexity. Zbl 0819.05035 Cockayne, E. J.; Mynhardt, C. M.; Yu, Bo 7 1995 On generalised minimal domination parameters for paths. Zbl 0744.05056 Bollobás, Béla; Cockayne, E. J.; Mynhardt, C. M. 7 1990 Independence and domination in 3-connected cubic graphs. Zbl 0763.05094 Cockayne, E. J.; Mynhardt, C. M. 7 1991 Universal minimal total dominating functions in graphs. Zbl 0804.90122 Cockayne, E. J.; Mynhardt, C. M.; Yu, Bo 7 1994 Eternal total domination in graphs. Zbl 1289.05351 Klostermeyer, William F.; Mynhardt, Christina M. 7 2012 On the sizes of least common multiples of several pairs of graphs. Zbl 0881.05104 Favaron, O.; Mynhardt, C. M. 6 1996 Trees with domination subdivision number one. Zbl 1153.05018 Benecke, S.; Mynhardt, C. M. 6 2008 Domination in prisms of graphs: universal fixers. Zbl 1284.05199 Mynhardt, C. M.; Xu, Zhixia 6 2009 The irredundant Ramsey number s(3,6). Zbl 0707.05047 Brewster, R. C.; Cockayne, E. J.; Mynhardt, C. M. 6 1990 On equality in an upper bound for domination parameters of graphs. Zbl 0872.05025 Favaron, O.; Mynhardt, C. M. 6 1997 Domination and irredundance in the queens’ graph. Zbl 0873.05055 Burger, A. P.; Cockayne, E. J.; Mynhardt, C. M. 6 1997 Domination numbers for the queen’s graph. Zbl 0805.05042 Burger, A. P.; Mynhardt, C. M.; Cockayne, E. J. 6 1994 Bounds for independent Roman domination in graphs. Zbl 1247.05154 Targhi, E. Ebrahimi; Rad, N. Jafari; Mynhardt, C. M.; Wu, Y. 6 2012 A class of trees with equal broadcast and domination numbers. Zbl 1276.05029 Mynhardt, C. M.; Wodlinger, J. 6 2013 Diameter of paired domination edge-critical graphs. Zbl 1169.05032 Edwards, M.; Gibson, R. G.; Henning, M. A.; Mynhardt, C. M. 5 2008 On 1-dependent Ramsey numbers for graphs. Zbl 0932.05061 Cockayne, E. J.; Mynhardt, C. M. 5 1999 On the sizes of least common multiples of paths versus complete graphs. Zbl 0822.05062 Mynhardt, C. M.; Saba, F. 5 1994 On the difference between the domination and independent domination numbers of cubic graphs. Zbl 0840.05038 Mynhardt, Christine 5 1991 Irredundant Ramsey numbers for graphs. Zbl 0692.05044 Brewster, R. C.; Cockayne, E. J.; Mynhardt, C. M. 5 1989 Queens graphs for chessboards on the torus. Zbl 0979.05080 Burger, A. P.; Mynhardt, C. M.; Cockayne, E. J. 5 2001 The depression of a graph. Zbl 1111.05086 Cockayne, E. J.; Geldenhuys, G.; Grobler, P. J. P.; Mynhardt, C. M.; van Vuuren, J. H. 5 2006 Altitude of \(K_{3,n}\). Zbl 1073.05062 Cochayne, E. J.; Mynhardt, C. M. 5 2005 More trees with equal broadcast and domination numbers. Zbl 1309.05139 Lunney, S.; Mynhardt, C. M. 5 2015 On graphs with a unique least common multiple. Zbl 0933.05131 Chartrand, Gary; Kubicki, Grzegorz; Mynhardt, Christina M.; Saba, Farrokh 4 1997 Symmetry and domination in queens graphs. Zbl 0954.05034 Burger, A. P.; Mynhardt, C. M. 4 2000 Properties of dominating sets of the queens graph \(Q_{4k+3}\). Zbl 0955.05076 Burger, A. P.; Mynhardt, C. M. 4 2000 A characterisation of universal minimal total dominating functions in trees. Zbl 0824.05034 Cockayne, E. J.; Mynhardt, C. M. 4 1995 On least common multiples of digraphs. Zbl 0853.05060 Chartrand, Gary; Mynhardt, Christina M.; Saba, Farrokh 4 1996 Irredundant and perfect neighbourhood sets in trees. Zbl 0955.05027 Cockayne, E. J.; Hedetniemi, S. M.; Hedetniemi, S. T.; Mynhardt, C. M. 4 1998 Vertex criticality for upper domination and irredundance. Zbl 0992.05057 Grobler, P. J. P.; Mynhardt, C. M. 4 2001 Nordhaus-Gaddum results for CO-irredundance in graphs. Zbl 0948.05037 Cockayne, E. J.; McCrea, D.; Mynhardt, C. M. 4 2000 The irredundant Ramsey number s(3,7). Zbl 0728.05047 Cockayne, E. J.; Hattingh, J. H.; Mynhardt, C. M. 4 1991 Generalised maximal independence parameters for paths and cycles. Zbl 0757.05097 Cockayne, E. J.; MacGillivray, G.; Mynhardt, C. M. 4 1990 The irredundant Ramsey number \(s(4,4)\). Zbl 0771.05070 Cockayne, E. J.; Exoo, G.; Hattingh, J. H.; Mynhardt, C. M. 4 1992 Domination and irredundance in cubic graphs. Zbl 0873.05056 Cockayne, E. J.; Mynhardt, C. M. 4 1997 Domination, eternal domination, and clique covering. Zbl 1311.05151 Klostermeyer, William F.; Mynhardt, C. M. 4 2015 An improved upper bound for queens domination numbers. Zbl 1015.05066 Burger, A. P.; Mynhardt, C. M. 4 2003 An upper bound for the minimum number of queens covering the \(n {\times} n\) chessboard. Zbl 0993.05105 Burger, A. P.; Mynhardt, C. M. 4 2002 On \(k\)-total dominating graphs. Zbl 1411.05196 Alikhani, S.; Fatehi, David; Mynhardt, C. M. 4 2019 k-minimal domination numbers of cycles. Zbl 0667.05053 Mynhardt, C. M.; Cockayne, E. J. 3 1987 Trees with depression three. Zbl 1149.05042 Mynhardt, C. M. 3 2008 Paired domination in prisms of graphs. Zbl 1238.05201 Mynhardt, Christina M.; Schurch, Mark 3 2011 Queens on hexagonal boards. Zbl 0944.05068 Burger, A. P.; Mynhardt, C. M. 3 1999 On a conjecture concerning irredundant and perfect neighbourhood sets in graphs. Zbl 0949.05060 Cockayne, E. J.; Mynhardt, C. M. 3 1999 On two conjectures concerning 3-domination-critical graphs. Zbl 0952.05054 Mynhardt, C. M. 3 1998 Upper domination parameters and edge-critical graphs. Zbl 0959.05084 Grobler, P. J. P.; Mynhardt, C. M. 3 2000 Convexity of minimal dominating functions of trees. Zbl 0839.05030 Cockayne, E. J.; McGillivray, G.; Mynhardt, C. M. 3 1995 Domination parameters and edge-removal-critical graphs. Zbl 0973.05056 Grobler, P. J. P.; Mynhardt, C. M. 3 2001 Domination of generalized Cartesian products. Zbl 1201.05069 Benecke, S.; Mynhardt, C. M. 3 2010 Total domination in claw-free cubic graphs. Zbl 1011.05043 Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. 3 2002 A lower bound for the depression of trees. Zbl 1094.05018 Cockayne, E. J.; Mynhardt, C. M. 3 2006 Open irredundance and maximum degree in graphs. Zbl 1207.05095 Cockayne, E. J.; Favaron, O.; Finbow, S.; Mynhardt, C. M. 3 2008 On the product of \(k\)-minimal domination numbers of a graph and its complement. Zbl 0745.05055 Cockayne, E. J.; Mynhardt, C. M. 3 1990 Domination sequences of graphs. Zbl 0772.05051 Cockayne, E. J.; Mynhardt, C. M. 3 1992 The irredundant Ramsey number \(s(3,3,3)=13\). Zbl 0807.05057 Cockayne, E. J.; Mynhardt, C. M. 3 1994 Critical graphs with respect to vertex identification. Zbl 1170.05035 Frick, Marietjie; Fricke, Gerd H.; Mynhardt, Christina M.; Skaggs, R. Duane 3 2008 Changing upper irredundance by edge addition. Zbl 1023.05106 Cockayne, E. J.; Favaron, O.; Goddard, W.; Grobler, P. J. P.; Mynhardt, C. M. 3 2003 Irredundance trees of diameter 3. Zbl 1497.05061 Mynhardt, C. M.; Roux, A. 1 2022 Irredundance graphs. Zbl 1498.05188 Mynhardt, C. M.; Roux, A. 1 2022 Irredundance. Zbl 1522.05356 Mynhardt, C. M.; Roux, A. 1 2021 Block graphs with large paired domination multisubdivision number. Zbl 1458.05202 Mynhardt, Christina M.; Raczek, Joanna 1 2021 Reconfiguration of colourings and dominating sets in graphs. Zbl 1451.05118 Mynhardt, C. M.; Nasserasr, S. 16 2020 Eternal and secure domination in graphs. Zbl 07445760 Klostermeyer, William F.; Mynhardt, C. M. 1 2020 Total Roman domination edge-supercritical and edge-removal-supercritical graphs. Zbl 1453.05092 Mynhardt, C. M.; Ogden, S. E. A. 1 2020 Connected \(k\)-dominating graphs. Zbl 1400.05177 Mynhardt, C. M.; Teshima, L. E.; Roux, A. 9 2019 On \(k\)-total dominating graphs. Zbl 1411.05196 Alikhani, S.; Fatehi, David; Mynhardt, C. M. 4 2019 Total Roman domination edge-critical graphs. Zbl 1432.05072 Lampman, Chloe; Mynhardt, Kieka (C. M.); Ogden, Shannon 2 2019 Subgraph-avoiding minimum decycling sets and \(k\)-conversion sets in graphs. Zbl 1419.05072 Francis, M. D.; Mynhardt, C. M.; Wodlinger, Jane L. 1 2019 A note on some variations of the \(\gamma\)-graph. Zbl 1390.05173 Mynhardt, C. M.; Teshima, L. E. 8 2018 Broadcasts and multipackings in trees. Zbl 1383.05242 Mynhardt, C. M.; Teshima, L. E. 17 2017 Broadcasts in graphs: diametrical trees. Zbl 1375.05195 Gemmrich, L.; Mynhardt, C. M. 2 2017 Dominating and irredundant broadcasts in graphs. Zbl 1355.05189 Mynhardt, C. M.; Roux, A. 2 2017 Protecting a graph with mobile guards. Zbl 1461.05157 Klostermeyer, William F.; Mynhardt, C. M. 28 2016 More trees with equal broadcast and domination numbers. Zbl 1309.05139 Lunney, S.; Mynhardt, C. M. 5 2015 Domination, eternal domination, and clique covering. Zbl 1311.05151 Klostermeyer, William F.; Mynhardt, C. M. 4 2015 Uniquely radial trees. Zbl 1326.05109 Mynhardt, C. M.; Wodlinger, J. 2 2015 A dynamic domination problem in trees. Zbl 1463.05406 Klostermeyer, William; Mynhardt, Christina 1 2015 On the difference between broadcast and multipacking numbers of graphs. Zbl 1300.05224 Hartnell, B. L.; Mynhardt, C. M. 8 2014 Independent protection in graphs. Zbl 1298.05248 Hartnell, B. L.; Mynhardt, C. M. 2 2014 Secure paired domination in graphs. Zbl 1309.05135 Kang, Jian; Mynhardt, C. M. 1 2014 New bounds for the broadcast domination number of a graph. Zbl 1266.05109 Brewster, Richard C.; Mynhardt, Christina M.; Teshima, Laura E. 13 2013 Eternal protection in grid graphs. Zbl 1300.05177 Goldwasser, John L.; Klostermeyer, William F.; Mynhardt, C. M. 13 2013 A class of trees with equal broadcast and domination numbers. Zbl 1276.05029 Mynhardt, C. M.; Wodlinger, J. 6 2013 A class of graphs with depression three. Zbl 1277.05083 Mynhardt, C. M.; Schurch, M. 1 2013 Vertex covers and eternal dominating sets. Zbl 1408.05099 Klostermeyer, William F.; Mynhardt, C. M. 9 2012 Eternal total domination in graphs. Zbl 1289.05351 Klostermeyer, William F.; Mynhardt, Christina M. 7 2012 Bounds for independent Roman domination in graphs. Zbl 1247.05154 Targhi, E. Ebrahimi; Rad, N. Jafari; Mynhardt, C. M.; Wu, Y. 6 2012 Graphs with equal eternal vertex cover and eternal domination numbers. Zbl 1223.05232 Klostermeyer, William F.; Mynhardt, C. M. 14 2011 Broadcasts and domination in trees. Zbl 1222.05196 Cockayne, E. J.; Herke, S.; Mynhardt, C. M. 11 2011 Paired domination in prisms of graphs. Zbl 1238.05201 Mynhardt, Christina M.; Schurch, Mark 3 2011 Domination of generalized Cartesian products. Zbl 1201.05069 Benecke, S.; Mynhardt, C. M. 3 2010 Regular graphs are not universal fixers. Zbl 1216.05098 Burger, A. P.; Mynhardt, C. M. 2 2010 Radial trees. Zbl 1221.05051 Herke, S.; Mynhardt, C. M. 17 2009 Secure domination critical graphs. Zbl 1189.05126 Grobler, P. J. P.; Mynhardt, C. M. 15 2009 Edge protection in graphs. Zbl 1207.05141 Klostermeyer, William F.; Mynhardt, C. M. 14 2009 Domination in prisms of graphs: universal fixers. Zbl 1284.05199 Mynhardt, C. M.; Xu, Zhixia 6 2009 Claw-free graphs are not universal fixers. Zbl 1219.05116 Cockayne, E. J.; Gibson, R. G.; Mynhardt, C. M. 2 2009 Secure domination and secure total domination in graphs. Zbl 1156.05043 Klostermeyer, William F.; Mynhardt, Christina M. 32 2008 The diameter of paired-domination vertex critical graphs. Zbl 1174.05093 Henning, Michael A.; Mynhardt, Christina M. 9 2008 Trees with domination subdivision number one. Zbl 1153.05018 Benecke, S.; Mynhardt, C. M. 6 2008 Diameter of paired domination edge-critical graphs. Zbl 1169.05032 Edwards, M.; Gibson, R. G.; Henning, M. A.; Mynhardt, C. M. 5 2008 Trees with depression three. Zbl 1149.05042 Mynhardt, C. M. 3 2008 Open irredundance and maximum degree in graphs. Zbl 1207.05095 Cockayne, E. J.; Favaron, O.; Finbow, S.; Mynhardt, C. M. 3 2008 Critical graphs with respect to vertex identification. Zbl 1170.05035 Frick, Marietjie; Fricke, Gerd H.; Mynhardt, Christina M.; Skaggs, R. Duane 3 2008 Secure total domination in graphs. Zbl 1183.05055 Benecke, S.; Cockayne, E. J.; Mynhardt, C. M. 14 2007 Construction of trees and graphs with equal domination parameters. Zbl 1104.05053 Dorfling, Michael; Goddard, Wayne; Henning, Michael A.; Mynhardt, C. M. 26 2006 The depression of a graph. Zbl 1111.05086 Cockayne, E. J.; Geldenhuys, G.; Grobler, P. J. P.; Mynhardt, C. M.; van Vuuren, J. H. 5 2006 A lower bound for the depression of trees. Zbl 1094.05018 Cockayne, E. J.; Mynhardt, C. M. 3 2006 Excellent trees and secure domination. Zbl 1071.05058 Mynhardt, C. M.; Swart, H. C.; Ungerer, E. 22 2005 Altitude of small complete and complete bipartite graphs. Zbl 1080.05046 Burger, A. P.; Cockayne, E. J.; Mynhardt, C. M. 8 2005 Altitude of regular graphs with girth at least five. Zbl 1062.05131 Mynhardt, C. M.; Burger, A. P.; Clark, T. C.; Falvai, B.; Henderson, N. D. R. 8 2005 Altitude of \(K_{3,n}\). Zbl 1073.05062 Cochayne, E. J.; Mynhardt, C. M. 5 2005 Infinite order domination in graphs. Zbl 1052.05054 Burger, A. P.; Cockayne, E. J.; Gründlingh, W. R.; Mynhardt, C. M.; van Vuuren, J. H.; Winterbach, W. 39 2004 Finite order domination in graphs. Zbl 1052.05053 Burger, A. P.; Cockayne, E. J.; Gründlingh, W. R.; Mynhardt, C. M.; van Vuuren, J. H.; Winterbach, W. 21 2004 On the domination number of prisms of graphs. Zbl 1064.05111 Burger, Alewyn; Mynhardt, Christina M.; Weakley, William D. 9 2004 Regular solutions of the \(n\)-queens problem on the torus. Zbl 1052.05057 Burger, A. P.; Mynhardt, C. M.; Cockayne, E. J. 1 2004 Altitude of 4-regular circulants. Zbl 1073.05061 Clark, T. C.; Falvai, B.; Hendersonand, D. R.; Mynhardt, C. M. 1 2004 Total domination in \(K_ r\)-covered graphs. Zbl 1078.05063 Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. 1 2004 Secure domination, weak Roman domination and forbidden subgraphs. Zbl 1051.05065 Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. 37 2003 Total domination edge critical graphs with minimum diameter. Zbl 1072.05557 van der Merwe, L. C.; Mynhardt, C. M.; Haynes, T. W. 13 2003 Vertices contained in all or in no minimum total dominating set of a tree. Zbl 1013.05054 Cockayne, Ernest J.; Henning, Michael A.; Mynhardt, Christina M. 11 2003 An improved upper bound for queens domination numbers. Zbl 1015.05066 Burger, A. P.; Mynhardt, C. M. 4 2003 Changing upper irredundance by edge addition. Zbl 1023.05106 Cockayne, E. J.; Favaron, O.; Goddard, W.; Grobler, P. J. P.; Mynhardt, C. M. 3 2003 The domination number of the toroidal queens graph of size \(3k\times 3k\). Zbl 1030.05094 Burger, A. P.; Mynhardt, C. M.; Weakley, William D. 2 2003 Upper bounds for the domination numbers of toroidal queens graphs. Zbl 1035.05066 Mynhardt, Christina M. 2 2003 An upper bound for the minimum number of queens covering the \(n {\times} n\) chessboard. Zbl 0993.05105 Burger, A. P.; Mynhardt, C. M. 4 2002 Total domination in claw-free cubic graphs. Zbl 1011.05043 Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. 3 2002 Total domination edge critical graphs with maximum diameter. Zbl 1007.05077 van der Merwe, Lucas C.; Mynhardt, Cristine M.; Haynes, Theresa W. 16 2001 Queens graphs for chessboards on the torus. Zbl 0979.05080 Burger, A. P.; Mynhardt, C. M.; Cockayne, E. J. 5 2001 Vertex criticality for upper domination and irredundance. Zbl 0992.05057 Grobler, P. J. P.; Mynhardt, C. M. 4 2001 Domination parameters and edge-removal-critical graphs. Zbl 0973.05056 Grobler, P. J. P.; Mynhardt, C. M. 3 2001 Properties of queens graphs and the irredundance number of \(Q_7\). Zbl 0966.05054 Cockayne, E. J.; Mynhardt, C. M. 2 2001 Ramsey properties of generalised irredundant sets in graphs. Zbl 0977.05089 Cockayne, E. J.; Favaron, O.; Grobler, P. J. P.; Mynhardt, C. M.; Puech, J. 2 2001 Irredundance-edge-removal-critical graphs. Zbl 1012.05126 Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. 1 2001 Total domination in graphs with minimum degree three. Zbl 0945.05047 Favaron, Odile; Henning, Michael A.; Mynhart, Christina M.; Puech, Joël 24 2000 A characterization of \((\gamma,i)\)-trees. Zbl 0949.05059 Cockayne, E. J.; Favaron, O.; Mynhardt, C. M.; Puech, J. 12 2000 Symmetry and domination in queens graphs. Zbl 0954.05034 Burger, A. P.; Mynhardt, C. M. 4 2000 Properties of dominating sets of the queens graph \(Q_{4k+3}\). Zbl 0955.05076 Burger, A. P.; Mynhardt, C. M. 4 2000 Nordhaus-Gaddum results for CO-irredundance in graphs. Zbl 0948.05037 Cockayne, E. J.; McCrea, D.; Mynhardt, C. M. 4 2000 Upper domination parameters and edge-critical graphs. Zbl 0959.05084 Grobler, P. J. P.; Mynhardt, C. M. 3 2000 The CO-irredundant Ramsey number \(t(4,7)\). Zbl 0956.05073 Cockayne, E. J.; Mynhardt, C. M.; Simmons, J. 2 2000 Small irredundance numbers for queens graphs. Zbl 0959.05083 Burger, A. P.; Mynhardt, C. M. 2 2000 Vertices contained in every minimum dominating set of a tree. Zbl 0931.05063 Mynhardt, C. M. 21 1999 3-domination critical graphs with arbitrary independent domination numbers. Zbl 0944.05074 van der Merwe, L. C.; Mynhardt, C. M.; Haynes, T. W. 11 1999 On 1-dependent Ramsey numbers for graphs. Zbl 0932.05061 Cockayne, E. J.; Mynhardt, C. M. 5 1999 Queens on hexagonal boards. Zbl 0944.05068 Burger, A. P.; Mynhardt, C. M. 3 1999 On a conjecture concerning irredundant and perfect neighbourhood sets in graphs. Zbl 0949.05060 Cockayne, E. J.; Mynhardt, C. M. 3 1999 Total domination edge critical graphs. Zbl 0918.05069 van der Merwe, L. C.; Mynhardt, C. M.; Haynes, T. W. 40 1998 Criticality index of total domination. Zbl 0951.05081 van der Merwe, Lucas C.; Mynhardt, Christina M.; Haynes, Teresa W. 13 1998 Irredundant and perfect neighbourhood sets in trees. Zbl 0955.05027 Cockayne, E. J.; Hedetniemi, S. M.; Hedetniemi, S. T.; Mynhardt, C. M. 4 1998 On two conjectures concerning 3-domination-critical graphs. Zbl 0952.05054 Mynhardt, C. M. 3 1998 Packing, perfect neighbourhood, irredundant and \(R\)-annihilated sets in graphs. Zbl 0916.05042 Cockayne, E. J.; Favaron, O.; Puech, J.; Mynhardt, C. M. 2 1998 Domination-related parameters. Zbl 0907.05027 Cockayne, E. J.; Mynhardt, C. M. 2 1998 An inequality chain of domination parameters for trees. Zbl 0914.05058 Cockayne, E. J.; Favaron, O.; Puech, J.; Mynhardt, C. M. 1 1998 Irredundance and maximum degree in graphs. Zbl 0881.05068 Cockayne, E. J.; Mynhardt, C. M. 11 1997 On equality in an upper bound for domination parameters of graphs. Zbl 0872.05025 Favaron, O.; Mynhardt, C. M. 6 1997 Domination and irredundance in the queens’ graph. Zbl 0873.05055 Burger, A. P.; Cockayne, E. J.; Mynhardt, C. M. 6 1997 ...and 45 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 613 Authors 81 Henning, Michael Anthony 45 Mynhardt, Christina Magdalena 28 Haynes, Teresa W. 21 Cockayne, Ernest J. 14 Hedetniemi, Stephen Travis 14 Klostermeyer, William F. 13 Favaron, Odile 12 Chellali, Mustapha 12 Yeo, Anders 11 MacGillivray, Gary 10 Goddard, Wayne Dean 10 Hattingh, Johannes H. 10 Sheikholeslami, Seyed Mahmoud 9 Burger, Alewyn Petrus 9 Jafari Rad, Nader 9 Southey, Justin 8 Dettlaff, Magda 8 McRae, Alice A. 8 Rautenbach, Dieter 7 Lemańska, Magdalena 7 Rodríguez-Velazquez, Juan Alberto 7 van der Merwe, Lucas C. 6 Amjadi, Jafar 6 Cabrera Martínez, Abel 6 Desormeaux, Wyatt J. 6 Ekim, Tınaz 6 Messinger, Margaret-Ellen 6 Pushpam, P. Roushini Leely 6 Yero, Ismael Gonzalez 5 Arumugam, Subramanian 5 Finbow, Stephen 5 Foucaud, Florent 5 Gimbel, John G. 5 Haas, Ruth 5 Hedetniemi, Sandra Lee Mitchell 5 Kang, Liying 5 Raczek, Joanna 5 Shan, Erfang 5 Xu, Baogen 4 Araki, Toru 4 Babu, Jasine 4 Chen, Xuegang 4 Dantas, Simone 4 de Villiers, Anton Pierre 4 Fernau, Henning 4 Kratsch, Dieter 4 Lu, Changhong 4 Mc Inerney, Fionn 4 Mondal, Sukumar 4 Nisse, Nicolas 4 Pandey, Arti 4 Pérennes, Stéphane 4 Sun, Liang 4 Suseendran, Chitra 4 Topp, Jerzy 4 van Vuuren, Jan Harm 4 Volkmann, Lutz 4 Xu, Junming 3 Ahangar, Hossein Abdollahzadeh 3 Barman, Sambhu Charan 3 Bessy, Stéphane 3 Bouchemakh, Isma 3 Branković, Ljiljana 3 Brešar, Boštjan 3 Brewster, Richard C. 3 Brown, Jason Ira 3 Chang, Gerard Jennhwa 3 Charon, Irène 3 Cohen, Nathann 3 Dorbec, Paul 3 Ebrahimi, Nafiseh 3 Golovach, Petr A. 3 Grobler, P. J. P. 3 Hartnell, Bert L. 3 Hu, Futao 3 Hudry, Olivier 3 Jha, Anupriya 3 Kassem, Ali 3 Klavžar, Sandi 3 Kusum 3 Laskar, Renu Chakravarti 3 Li, Zepeng 3 Liedloff, Mathieu 3 Lobstein, Antoine-Christophe 3 Löwenstein, Christian 3 Lu, You 3 Martins, Nicolas Almeida 3 Pal, Madhumangal 3 Perez, Anthony 3 Prabhakaran, Veena 3 Puech, Joël 3 Reji, T. 3 Sampaio, Rudini Menezes 3 Shaheen, Ramy S. 3 Slater, Peter James 3 Virgile, Virgélot 3 Wang, Changping 3 Xu, Jin 3 Yi, Eunjeong 3 Zuazua, Rita Esther ...and 513 more Authors all top 5 Cited in 82 Serials 105 Discrete Mathematics 77 Discrete Applied Mathematics 28 Graphs and Combinatorics 18 Journal of Combinatorial Optimization 17 Discussiones Mathematicae. Graph Theory 16 Discrete Mathematics, Algorithms and Applications 14 Theoretical Computer Science 12 AKCE International Journal of Graphs and Combinatorics 11 Journal of Graph Theory 11 Quaestiones Mathematicae 10 Information Processing Letters 7 The Australasian Journal of Combinatorics 6 Journal of Discrete Mathematical Sciences & Cryptography 6 Central European Journal of Mathematics 6 Discrete Optimization 5 Czechoslovak Mathematical Journal 5 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 European Journal of Combinatorics 4 The Electronic Journal of Combinatorics 4 Advances and Applications in Discrete Mathematics 4 Electronic Journal of Graph Theory and Applications 3 Algorithmica 3 Applied Mathematics Letters 3 Opuscula Mathematica 3 Journal of Applied Mathematics 3 Journal of Applied Mathematics and Computing 3 Transactions on Combinatorics 3 AIMS Mathematics 2 Journal of Combinatorial Theory. Series B 2 Annals of Combinatorics 2 Asian-European Journal of Mathematics 2 Acta Universitatis Sapientiae. Informatica 2 Cryptography and Communications 2 RAIRO. Theoretical Informatics and Applications 2 Communications in Combinatorics and Optimization 2 Ural Mathematical Journal 1 Computers & Mathematics with Applications 1 Indian Journal of Pure & Applied Mathematics 1 Israel Journal of Mathematics 1 Rocky Mountain Journal of Mathematics 1 Applied Mathematics and Computation 1 International Journal of Game Theory 1 Networks 1 Advances in Applied Mathematics 1 Operations Research Letters 1 Combinatorica 1 Acta Mathematica Hungarica 1 Acta Mathematicae Applicatae Sinica. 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Discrete Mathematics Letters 1 La Matematica all top 5 Cited in 13 Fields 453 Combinatorics (05-XX) 70 Computer science (68-XX) 23 Operations research, mathematical programming (90-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Information and communication theory, circuits (94-XX) 4 Manifolds and cell complexes (57-XX) 3 Commutative algebra (13-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Convex and discrete geometry (52-XX) 1 Probability theory and stochastic processes (60-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.