Edit Profile (opens in new tab) Mynhardt, Christina Magdalena Compute Distance To: Compute Author ID: mynhardt.christina-m Published as: Mynhardt, C. M.; Mynhardt, Christina M.; Mynhardt, Christine; Mynhardt, Kieka (C. M.); Mynhardt, Christina; Mynhardt, Kieka; Mynhardt, C. M. Kieka; Mynhardt, Cristine M.; Mynhart, Christina M. more...less External Links: MGP · Wikidata · dblp Documents Indexed: 172 Publications since 1979 Co-Authors: 73 Co-Authors with 156 Joint Publications 1,212 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. 6 Haynes, Teresa W. 6 MacGillivray, Gary 6 Puech, Joël 6 van der Merwe, Lucas C. 5 Benecke, Stephen 5 Broere, Izak 5 Chartrand, Gary Theodore 5 Henning, Michael Anthony 5 Saba, Farrokh 5 Wodlinger, Jane L. 4 Brewster, Richard C. 4 Schurch, Mark 4 Teshima, Laura E. 3 Fricke, Gerd H. 3 Gibson, Richard G. jun. 3 Goddard, Wayne Dean 3 Hattingh, Johannes H. 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 Nasserasr, Shahla 2 Weakley, William D. 2 Winterbach, W. 1 Alikhani, Saeid 1 Ao, Shengmei 1 Bollobás, Béla 1 Boyer, Wanda 1 Breytenbach, Jean A. 1 Bullock, Frank 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 Jafari Rad, Nader 1 Kang, Jian 1 Kubicki, Grzegorz M. 1 Lampman, Chloe 1 Lesniak, Linda M. 1 Lorimer, P. J. 1 Lunney, S. 1 McCrea, Devon 1 McGillivray, Gary 1 Morrison, Laura 1 Neilson, L. 1 Oellermann, Ortrud R. 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 Wu, Yunjian 1 Xu, Zhixia all top 5 Serials 33 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 3 Discrete Applied Mathematics 3 Congressus Numerantium 3 AKCE International Journal of Graphs and Combinatorics 3 Involve 2 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 all top 5 Fields 169 Combinatorics (05-XX) 3 Operations research, mathematical programming (90-XX) 2 Number theory (11-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 139 Publications have been cited 889 times in 421 Documents Cited by ▼ Year ▼ Secure domination, weak Roman domination and forbidden subgraphs. Zbl 1051.05065Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. 35 2003 Infinite order domination in graphs. Zbl 1052.05054Burger, A. P.; Cockayne, E. J.; Gründlingh, W. R.; Mynhardt, C. M.; van Vuuren, J. H.; Winterbach, W. 35 2004 Total domination edge critical graphs. Zbl 0918.05069van der Merwe, L. C.; Mynhardt, C. M.; Haynes, T. W. 29 1998 Secure domination and secure total domination in graphs. Zbl 1156.05043Klostermeyer, William F.; Mynhardt, Christina M. 25 2008 Total domination in graphs with minimum degree three. Zbl 0945.05047Favaron, Odile; Henning, Michael A.; Mynhart, Christina M.; Puech, Joël 24 2000 Protecting a graph with mobile guards. Zbl 1461.05157Klostermeyer, William F.; Mynhardt, C. M. 24 2016 On a generalization of signed dominating functions of graphs. Zbl 0881.05060Cockayne, E. J.; Mynhardt, C. M. 23 1996 Construction of trees and graphs with equal domination parameters. Zbl 1104.05053Dorfling, Michael; Goddard, Wayne; Henning, Michael A.; Mynhardt, C. M. 23 2006 Finite order domination in graphs. Zbl 1052.05053Burger, A. P.; Cockayne, E. J.; Gründlingh, W. R.; Mynhardt, C. M.; van Vuuren, J. H.; Winterbach, W. 21 2004 Excellent trees and secure domination. Zbl 1071.05058Mynhardt, C. M.; Swart, H. C.; Ungerer, E. 20 2005 Generalized colorings of outerplanar and planar graphs. Zbl 0571.05017Broere, I.; Mynhardt, C. M. 19 1985 Reinforcement in graphs. Zbl 0862.05071Kok, J.; Mynhardt, C. M. 17 1990 Vertices contained in every minimum dominating set of a tree. Zbl 0931.05063Mynhardt, C. M. 17 1999 Total domination edge critical graphs with maximum diameter. Zbl 1007.05077van der Merwe, Lucas C.; Mynhardt, Cristine M.; Haynes, Theresa W. 16 2001 Radial trees. Zbl 1221.05051Herke, S.; Mynhardt, C. M. 14 2009 Secure domination critical graphs. Zbl 1189.05126Grobler, P. J. P.; Mynhardt, C. M. 14 2009 Total domination edge critical graphs with minimum diameter. Zbl 1072.05557van der Merwe, L. C.; Mynhardt, C. M.; Haynes, T. W. 13 2003 Criticality index of total domination. Zbl 0951.05081van der Merwe, Lucas C.; Mynhardt, Christina M.; Haynes, Teresa W. 13 1998 A characterization of \((\gamma,i)\)-trees. Zbl 0949.05059Cockayne, E. J.; Favaron, O.; Mynhardt, C. M.; Puech, J. 12 2000 The sequence of upper and lower domination, independence and irredundance numbers of a graph. Zbl 0788.05055Cockayne, E. J.; Mynhardt, C. M. 12 1993 On the product of upper irredundance numbers of a graph and its complement. Zbl 0672.05049Cockayne, E. J.; Mynhardt, C. M. 12 1989 Edge protection in graphs. Zbl 1207.05141Klostermeyer, William F.; Mynhardt, C. M. 11 2009 Graphs with equal eternal vertex cover and eternal domination numbers. Zbl 1223.05232Klostermeyer, William F.; Mynhardt, C. M. 11 2011 Secure total domination in graphs. Zbl 1183.05055Benecke, S.; Cockayne, E. J.; Mynhardt, C. M. 11 2007 Eternal protection in grid graphs. Zbl 1300.05177Goldwasser, John L.; Klostermeyer, William F.; Mynhardt, C. M. 11 2013 Vertices contained in all or in no minimum total dominating set of a tree. Zbl 1013.05054Cockayne, Ernest J.; Henning, Michael A.; Mynhardt, Christina M. 11 2003 Irredundance and maximum degree in graphs. Zbl 0881.05068Cockayne, E. J.; Mynhardt, C. M. 10 1997 3-domination critical graphs with arbitrary independent domination numbers. Zbl 0944.05074van der Merwe, L. C.; Mynhardt, C. M.; Haynes, T. W. 10 1999 Broadcasts and domination in trees. Zbl 1222.05196Cockayne, E. J.; Herke, S.; Mynhardt, C. M. 10 2011 The diameter of paired-domination vertex critical graphs. Zbl 1174.05093Henning, Michael A.; Mynhardt, Christina M. 9 2008 On a Nordhaus-Gaddum type problem for independent domination. Zbl 0820.05039Cockayne, E. J.; Fricke, G.; Mynhardt, C. M. 9 1995 New bounds for the broadcast domination number of a graph. Zbl 1266.05109Brewster, Richard C.; Mynhardt, Christina M.; Teshima, Laura E. 9 2013 Vertex covers and eternal dominating sets. Zbl 1408.05099Klostermeyer, William F.; Mynhardt, C. M. 8 2012 On the domination number of prisms of graphs. Zbl 1064.05111Burger, Alewyn; Mynhardt, Christina M.; Weakley, William D. 8 2004 Altitude of small complete and complete bipartite graphs. Zbl 1080.05046Burger, A. P.; Cockayne, E. J.; Mynhardt, C. M. 7 2005 Altitude of regular graphs with girth at least five. Zbl 1062.05131Mynhardt, C. M.; Burger, A. P.; Clark, T. C.; Falvai, B.; Henderson, N. D. R. 7 2005 Eternal total domination in graphs. Zbl 1289.05351Klostermeyer, William F.; Mynhardt, Christina M. 7 2012 Properties of minimal dominating functions of graphs. Zbl 0840.05090Cockayne, E. J.; Fricke, G.; Hedetniemi, S. T.; Mynhardt, C. M. 7 1995 Domination critical graphs with higher independent domination numbers. Zbl 0852.05053Ao, S.; Cockayne, E. J.; MacGillivray, G.; Mynhardt, C. M. 7 1996 Broadcasts and multipackings in trees. Zbl 1383.05242Mynhardt, C. M.; Teshima, L. E. 7 2017 Domination in prisms of graphs: universal fixers. Zbl 1284.05199Mynhardt, C. M.; Xu, Zhixia 6 2009 On generalised minimal domination parameters for paths. Zbl 0744.05056Bollobás, Béla; Cockayne, E. J.; Mynhardt, C. M. 6 1990 Independence and domination in 3-connected cubic graphs. Zbl 0763.05094Cockayne, E. J.; Mynhardt, C. M. 6 1991 On equality in an upper bound for domination parameters of graphs. Zbl 0872.05025Favaron, O.; Mynhardt, C. M. 6 1997 Domination and irredundance in the queens’ graph. Zbl 0873.05055Burger, A. P.; Cockayne, E. J.; Mynhardt, C. M. 6 1997 Universal minimal total dominating functions in graphs. Zbl 0804.90122Cockayne, E. J.; Mynhardt, C. M.; Yu, Bo 6 1994 Domination numbers for the queen’s graph. Zbl 0805.05042Burger, A. P.; Mynhardt, C. M.; Cockayne, E. J. 6 1994 Total dominating functions in trees: Minimality and convexity. Zbl 0819.05035Cockayne, E. J.; Mynhardt, C. M.; Yu, Bo 6 1995 Trees with domination subdivision number one. Zbl 1153.05018Benecke, S.; Mynhardt, C. M. 6 2008 On the difference between broadcast and multipacking numbers of graphs. Zbl 1300.05224Hartnell, B. L.; Mynhardt, C. M. 6 2014 The irredundant Ramsey number s(3,6). Zbl 0707.05047Brewster, R. C.; Cockayne, E. J.; Mynhardt, C. M. 6 1990 An improved upper bound for queens domination numbers. Zbl 1015.05066Burger, A. P.; Mynhardt, C. M. 5 2003 Altitude of \(K_{3,n}\). Zbl 1073.05062Cochayne, E. J.; Mynhardt, C. M. 5 2005 On the sizes of least common multiples of several pairs of graphs. Zbl 0881.05104Favaron, O.; Mynhardt, C. M. 5 1996 On the difference between the domination and independent domination numbers of cubic graphs. Zbl 0840.05038Mynhardt, Christine 5 1991 A class of trees with equal broadcast and domination numbers. Zbl 1276.05029Mynhardt, C. M.; Wodlinger, J. 5 2013 Irredundant Ramsey numbers for graphs. Zbl 0692.05044Brewster, R. C.; Cockayne, E. J.; Mynhardt, C. M. 5 1989 The depression of a graph. Zbl 1111.05086Cockayne, E. J.; Geldenhuys, G.; Grobler, P. J. P.; Mynhardt, C. M.; van Vuuren, J. H. 5 2006 Diameter of paired domination edge-critical graphs. Zbl 1169.05032Edwards, M.; Gibson, R. G.; Henning, M. A.; Mynhardt, C. M. 5 2008 A note on some variations of the \(\gamma\)-graph. Zbl 1390.05173Mynhardt, C. M.; Teshima, L. E. 5 2018 An upper bound for the minimum number of queens covering the \(n {\times} n\) chessboard. Zbl 0993.05105Burger, A. P.; Mynhardt, C. M. 5 2002 Bounds for independent Roman domination in graphs. Zbl 1247.05154Targhi, E. Ebrahimi; Rad, N. Jafari; Mynhardt, C. M.; Wu, Y. 4 2012 Vertex criticality for upper domination and irredundance. Zbl 0992.05057Grobler, P. J. P.; Mynhardt, C. M. 4 2001 Queens graphs for chessboards on the torus. Zbl 0979.05080Burger, A. P.; Mynhardt, C. M.; Cockayne, E. J. 4 2001 Properties of dominating sets of the queens graph \(Q_{4k+3}\). Zbl 0955.05076Burger, A. P.; Mynhardt, C. M. 4 2000 Irredundant and perfect neighbourhood sets in trees. Zbl 0955.05027Cockayne, E. J.; Hedetniemi, S. M.; Hedetniemi, S. T.; Mynhardt, C. M. 4 1998 Generalised maximal independence parameters for paths and cycles. Zbl 0757.05097Cockayne, E. J.; MacGillivray, G.; Mynhardt, C. M. 4 1990 The irredundant Ramsey number \(s(4,4)\). Zbl 0771.05070Cockayne, E. J.; Exoo, G.; Hattingh, J. H.; Mynhardt, C. M. 4 1992 Domination and irredundance in cubic graphs. Zbl 0873.05056Cockayne, E. J.; Mynhardt, C. M. 4 1997 More trees with equal broadcast and domination numbers. Zbl 1309.05139Lunney, S.; Mynhardt, C. M. 4 2015 On 1-dependent Ramsey numbers for graphs. Zbl 0932.05061Cockayne, E. J.; Mynhardt, C. M. 4 1999 Nordhaus-Gaddum results for CO-irredundance in graphs. Zbl 0948.05037Cockayne, E. J.; McCrea, D.; Mynhardt, C. M. 4 2000 Symmetry and domination in queens graphs. Zbl 0954.05034Burger, A. P.; Mynhardt, C. M. 4 2000 On the sizes of least common multiples of paths versus complete graphs. Zbl 0822.05062Mynhardt, C. M.; Saba, F. 4 1994 The irredundant Ramsey number s(3,7). Zbl 0728.05047Cockayne, E. J.; Hattingh, J. H.; Mynhardt, C. M. 4 1991 Changing upper irredundance by edge addition. Zbl 1023.05106Cockayne, 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 1030.05094Burger, A. P.; Mynhardt, C. M.; Weakley, William D. 3 2003 Domination parameters and edge-removal-critical graphs. Zbl 0973.05056Grobler, P. J. P.; Mynhardt, C. M. 3 2001 Upper domination parameters and edge-critical graphs. Zbl 0959.05084Grobler, P. J. P.; Mynhardt, C. M. 3 2000 Connected \(k\)-dominating graphs. Zbl 1400.05177Mynhardt, C. M.; Teshima, L. E.; Roux, A. 3 2019 On the product of \(k\)-minimal domination numbers of a graph and its complement. Zbl 0745.05055Cockayne, E. J.; Mynhardt, C. M. 3 1990 Domination sequences of graphs. Zbl 0772.05051Cockayne, E. J.; Mynhardt, C. M. 3 1992 Domination, eternal domination, and clique covering. Zbl 1311.05151Klostermeyer, William F.; Mynhardt, C. M. 3 2015 The irredundant Ramsey number \(s(3,3,3)=13\). Zbl 0807.05057Cockayne, E. J.; Mynhardt, C. M. 3 1994 Domination of generalized Cartesian products. Zbl 1201.05069Benecke, S.; Mynhardt, C. M. 3 2010 On graphs with a unique least common multiple. Zbl 0933.05131Chartrand, Gary; Kubicki, Grzegorz; Mynhardt, Christina M.; Saba, Farrokh 3 1997 Queens on hexagonal boards. Zbl 0944.05068Burger, A. P.; Mynhardt, C. M. 3 1999 On a conjecture concerning irredundant and perfect neighbourhood sets in graphs. Zbl 0949.05060Cockayne, E. J.; Mynhardt, C. M. 3 1999 On two conjectures concerning 3-domination-critical graphs. Zbl 0952.05054Mynhardt, C. M. 3 1998 A characterisation of universal minimal total dominating functions in trees. Zbl 0824.05034Cockayne, E. J.; Mynhardt, C. M. 3 1995 Convexity of minimal dominating functions of trees. Zbl 0839.05030Cockayne, E. J.; McGillivray, G.; Mynhardt, C. M. 3 1995 On least common multiples of digraphs. Zbl 0853.05060Chartrand, Gary; Mynhardt, Christina M.; Saba, Farrokh 3 1996 Critical graphs with respect to vertex identification. Zbl 1170.05035Frick, Marietjie; Fricke, Gerd H.; Mynhardt, Christina M.; Skaggs, R. Duane 3 2008 Open irredundance and maximum degree in graphs. Zbl 1207.05095Cockayne, E. J.; Favaron, O.; Finbow, S.; Mynhardt, C. M. 3 2008 A lower bound for the depression of trees. Zbl 1094.05018Cockayne, E. J.; Mynhardt, C. M. 3 2006 Trees with depression three. Zbl 1149.05042Mynhardt, C. M. 3 2008 Reconfiguration of colourings and dominating sets in graphs. Zbl 1451.05118Mynhardt, C. M.; Nasserasr, S. 3 2020 Total domination in claw-free cubic graphs. Zbl 1011.05043Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. 3 2002 Minimality and convexity of dominating and related functions in graphs: A unifying theory. Zbl 0883.05078Cockayne, E. J.; Mynhardt, C. M. 2 1997 k-minimal domination numbers of cycles. Zbl 0667.05053Mynhardt, C. M.; Cockayne, E. J. 2 1987 Block graphs with large paired domination multisubdivision number. Zbl 1458.05202Mynhardt, Christina M.; Raczek, Joanna 1 2021 Reconfiguration of colourings and dominating sets in graphs. Zbl 1451.05118Mynhardt, C. M.; Nasserasr, S. 3 2020 Total Roman domination edge-supercritical and edge-removal-supercritical graphs. Zbl 1453.05092Mynhardt, C. M.; Ogden, S. E. A. 1 2020 Connected \(k\)-dominating graphs. Zbl 1400.05177Mynhardt, C. M.; Teshima, L. E.; Roux, A. 3 2019 Total Roman domination edge-critical graphs. Zbl 1432.05072Lampman, Chloe; Mynhardt, Kieka (C. M.); Ogden, Shannon 2 2019 On \(k\)-total dominating graphs. Zbl 1411.05196Alikhani, S.; Fatehi, David; Mynhardt, C. M. 1 2019 A note on some variations of the \(\gamma\)-graph. Zbl 1390.05173Mynhardt, C. M.; Teshima, L. E. 5 2018 Broadcasts and multipackings in trees. Zbl 1383.05242Mynhardt, C. M.; Teshima, L. E. 7 2017 Dominating and irredundant broadcasts in graphs. Zbl 1355.05189Mynhardt, C. M.; Roux, A. 2 2017 Broadcasts in graphs: diametrical trees. Zbl 1375.05195Gemmrich, L.; Mynhardt, C. M. 2 2017 Protecting a graph with mobile guards. Zbl 1461.05157Klostermeyer, William F.; Mynhardt, C. M. 24 2016 More trees with equal broadcast and domination numbers. Zbl 1309.05139Lunney, S.; Mynhardt, C. M. 4 2015 Domination, eternal domination, and clique covering. Zbl 1311.05151Klostermeyer, William F.; Mynhardt, C. M. 3 2015 Uniquely radial trees. Zbl 1326.05109Mynhardt, C. M.; Wodlinger, J. 2 2015 On the difference between broadcast and multipacking numbers of graphs. Zbl 1300.05224Hartnell, B. L.; Mynhardt, C. M. 6 2014 Independent protection in graphs. Zbl 1298.05248Hartnell, B. L.; Mynhardt, C. M. 1 2014 Secure paired domination in graphs. Zbl 1309.05135Kang, Jian; Mynhardt, C. M. 1 2014 Eternal protection in grid graphs. Zbl 1300.05177Goldwasser, John L.; Klostermeyer, William F.; Mynhardt, C. M. 11 2013 New bounds for the broadcast domination number of a graph. Zbl 1266.05109Brewster, Richard C.; Mynhardt, Christina M.; Teshima, Laura E. 9 2013 A class of trees with equal broadcast and domination numbers. Zbl 1276.05029Mynhardt, C. M.; Wodlinger, J. 5 2013 A class of graphs with depression three. Zbl 1277.05083Mynhardt, C. M.; Schurch, M. 1 2013 Vertex covers and eternal dominating sets. Zbl 1408.05099Klostermeyer, William F.; Mynhardt, C. M. 8 2012 Eternal total domination in graphs. Zbl 1289.05351Klostermeyer, William F.; Mynhardt, Christina M. 7 2012 Bounds for independent Roman domination in graphs. Zbl 1247.05154Targhi, E. Ebrahimi; Rad, N. Jafari; Mynhardt, C. M.; Wu, Y. 4 2012 Graphs with equal eternal vertex cover and eternal domination numbers. Zbl 1223.05232Klostermeyer, William F.; Mynhardt, C. M. 11 2011 Broadcasts and domination in trees. Zbl 1222.05196Cockayne, E. J.; Herke, S.; Mynhardt, C. M. 10 2011 Paired domination in prisms of graphs. Zbl 1238.05201Mynhardt, Christina M.; Schurch, Mark 2 2011 Domination of generalized Cartesian products. Zbl 1201.05069Benecke, S.; Mynhardt, C. M. 3 2010 Regular graphs are not universal fixers. Zbl 1216.05098Burger, A. P.; Mynhardt, C. M. 2 2010 Radial trees. Zbl 1221.05051Herke, S.; Mynhardt, C. M. 14 2009 Secure domination critical graphs. Zbl 1189.05126Grobler, P. J. P.; Mynhardt, C. M. 14 2009 Edge protection in graphs. Zbl 1207.05141Klostermeyer, William F.; Mynhardt, C. M. 11 2009 Domination in prisms of graphs: universal fixers. Zbl 1284.05199Mynhardt, C. M.; Xu, Zhixia 6 2009 Claw-free graphs are not universal fixers. Zbl 1219.05116Cockayne, E. J.; Gibson, R. G.; Mynhardt, C. M. 2 2009 Secure domination and secure total domination in graphs. Zbl 1156.05043Klostermeyer, William F.; Mynhardt, Christina M. 25 2008 The diameter of paired-domination vertex critical graphs. Zbl 1174.05093Henning, Michael A.; Mynhardt, Christina M. 9 2008 Trees with domination subdivision number one. Zbl 1153.05018Benecke, S.; Mynhardt, C. M. 6 2008 Diameter of paired domination edge-critical graphs. Zbl 1169.05032Edwards, M.; Gibson, R. G.; Henning, M. A.; Mynhardt, C. M. 5 2008 Critical graphs with respect to vertex identification. Zbl 1170.05035Frick, Marietjie; Fricke, Gerd H.; Mynhardt, Christina M.; Skaggs, R. Duane 3 2008 Open irredundance and maximum degree in graphs. Zbl 1207.05095Cockayne, E. J.; Favaron, O.; Finbow, S.; Mynhardt, C. M. 3 2008 Trees with depression three. Zbl 1149.05042Mynhardt, C. M. 3 2008 Secure total domination in graphs. Zbl 1183.05055Benecke, S.; Cockayne, E. J.; Mynhardt, C. M. 11 2007 Construction of trees and graphs with equal domination parameters. Zbl 1104.05053Dorfling, Michael; Goddard, Wayne; Henning, Michael A.; Mynhardt, C. M. 23 2006 The depression of a graph. Zbl 1111.05086Cockayne, 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 1094.05018Cockayne, E. J.; Mynhardt, C. M. 3 2006 Excellent trees and secure domination. Zbl 1071.05058Mynhardt, C. M.; Swart, H. C.; Ungerer, E. 20 2005 Altitude of small complete and complete bipartite graphs. Zbl 1080.05046Burger, A. P.; Cockayne, E. J.; Mynhardt, C. M. 7 2005 Altitude of regular graphs with girth at least five. Zbl 1062.05131Mynhardt, C. M.; Burger, A. P.; Clark, T. C.; Falvai, B.; Henderson, N. D. R. 7 2005 Altitude of \(K_{3,n}\). Zbl 1073.05062Cochayne, E. J.; Mynhardt, C. M. 5 2005 Infinite order domination in graphs. Zbl 1052.05054Burger, A. P.; Cockayne, E. J.; Gründlingh, W. R.; Mynhardt, C. M.; van Vuuren, J. H.; Winterbach, W. 35 2004 Finite order domination in graphs. Zbl 1052.05053Burger, 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 1064.05111Burger, Alewyn; Mynhardt, Christina M.; Weakley, William D. 8 2004 Altitude of 4-regular circulants. Zbl 1073.05061Clark, T. C.; Falvai, B.; Hendersonand, D. R.; Mynhardt, C. M. 1 2004 Total domination in \(K_ r\)-covered graphs. Zbl 1078.05063Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. 1 2004 Regular solutions of the \(n\)-queens problem on the torus. Zbl 1052.05057Burger, A. P.; Mynhardt, C. M.; Cockayne, E. J. 1 2004 Secure domination, weak Roman domination and forbidden subgraphs. Zbl 1051.05065Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. 35 2003 Total domination edge critical graphs with minimum diameter. Zbl 1072.05557van 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 1013.05054Cockayne, Ernest J.; Henning, Michael A.; Mynhardt, Christina M. 11 2003 An improved upper bound for queens domination numbers. Zbl 1015.05066Burger, A. P.; Mynhardt, C. M. 5 2003 Changing upper irredundance by edge addition. Zbl 1023.05106Cockayne, 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 1030.05094Burger, A. P.; Mynhardt, C. M.; Weakley, William D. 3 2003 Upper bounds for the domination numbers of toroidal queens graphs. Zbl 1035.05066Mynhardt, Christina M. 2 2003 An upper bound for the minimum number of queens covering the \(n {\times} n\) chessboard. Zbl 0993.05105Burger, A. P.; Mynhardt, C. M. 5 2002 Total domination in claw-free cubic graphs. Zbl 1011.05043Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. 3 2002 Total domination edge critical graphs with maximum diameter. Zbl 1007.05077van der Merwe, Lucas C.; Mynhardt, Cristine M.; Haynes, Theresa W. 16 2001 Vertex criticality for upper domination and irredundance. Zbl 0992.05057Grobler, P. J. P.; Mynhardt, C. M. 4 2001 Queens graphs for chessboards on the torus. Zbl 0979.05080Burger, A. P.; Mynhardt, C. M.; Cockayne, E. J. 4 2001 Domination parameters and edge-removal-critical graphs. Zbl 0973.05056Grobler, P. J. P.; Mynhardt, C. M. 3 2001 Properties of queens graphs and the irredundance number of \(Q_7\). Zbl 0966.05054Cockayne, E. J.; Mynhardt, C. M. 2 2001 Ramsey properties of generalised irredundant sets in graphs. Zbl 0977.05089Cockayne, E. J.; Favaron, O.; Grobler, P. J. P.; Mynhardt, C. M.; Puech, J. 2 2001 Irredundance-edge-removal-critical graphs. Zbl 1012.05126Cockayne, E. J.; Favaron, O.; Mynhardt, C. M. 1 2001 Total domination in graphs with minimum degree three. Zbl 0945.05047Favaron, Odile; Henning, Michael A.; Mynhart, Christina M.; Puech, Joël 24 2000 A characterization of \((\gamma,i)\)-trees. Zbl 0949.05059Cockayne, E. J.; Favaron, O.; Mynhardt, C. M.; Puech, J. 12 2000 Properties of dominating sets of the queens graph \(Q_{4k+3}\). Zbl 0955.05076Burger, A. P.; Mynhardt, C. M. 4 2000 Nordhaus-Gaddum results for CO-irredundance in graphs. Zbl 0948.05037Cockayne, E. J.; McCrea, D.; Mynhardt, C. M. 4 2000 Symmetry and domination in queens graphs. Zbl 0954.05034Burger, A. P.; Mynhardt, C. M. 4 2000 Upper domination parameters and edge-critical graphs. Zbl 0959.05084Grobler, P. J. P.; Mynhardt, C. M. 3 2000 The CO-irredundant Ramsey number \(t(4,7)\). Zbl 0956.05073Cockayne, E. J.; Mynhardt, C. M.; Simmons, J. 2 2000 Small irredundance numbers for queens graphs. Zbl 0959.05083Burger, A. P.; Mynhardt, C. M. 2 2000 Vertices contained in every minimum dominating set of a tree. Zbl 0931.05063Mynhardt, C. M. 17 1999 3-domination critical graphs with arbitrary independent domination numbers. Zbl 0944.05074van der Merwe, L. C.; Mynhardt, C. M.; Haynes, T. W. 10 1999 On 1-dependent Ramsey numbers for graphs. Zbl 0932.05061Cockayne, E. J.; Mynhardt, C. M. 4 1999 Queens on hexagonal boards. Zbl 0944.05068Burger, A. P.; Mynhardt, C. M. 3 1999 On a conjecture concerning irredundant and perfect neighbourhood sets in graphs. Zbl 0949.05060Cockayne, E. J.; Mynhardt, C. M. 3 1999 Total domination edge critical graphs. Zbl 0918.05069van der Merwe, L. C.; Mynhardt, C. M.; Haynes, T. W. 29 1998 Criticality index of total domination. Zbl 0951.05081van der Merwe, Lucas C.; Mynhardt, Christina M.; Haynes, Teresa W. 13 1998 Irredundant and perfect neighbourhood sets in trees. Zbl 0955.05027Cockayne, E. J.; Hedetniemi, S. M.; Hedetniemi, S. T.; Mynhardt, C. M. 4 1998 On two conjectures concerning 3-domination-critical graphs. Zbl 0952.05054Mynhardt, C. M. 3 1998 Packing, perfect neighbourhood, irredundant and \(R\)-annihilated sets in graphs. Zbl 0916.05042Cockayne, E. J.; Favaron, O.; Puech, J.; Mynhardt, C. M. 2 1998 Domination-related parameters. Zbl 0907.05027Cockayne, E. J.; Mynhardt, C. M. 1 1998 An inequality chain of domination parameters for trees. Zbl 0914.05058Cockayne, E. J.; Favaron, O.; Puech, J.; Mynhardt, C. M. 1 1998 Irredundance and maximum degree in graphs. Zbl 0881.05068Cockayne, E. J.; Mynhardt, C. M. 10 1997 On equality in an upper bound for domination parameters of graphs. Zbl 0872.05025Favaron, O.; Mynhardt, C. M. 6 1997 Domination and irredundance in the queens’ graph. Zbl 0873.05055Burger, A. P.; Cockayne, E. J.; Mynhardt, C. M. 6 1997 Domination and irredundance in cubic graphs. Zbl 0873.05056Cockayne, E. J.; Mynhardt, C. M. 4 1997 On graphs with a unique least common multiple. Zbl 0933.05131Chartrand, Gary; Kubicki, Grzegorz; Mynhardt, Christina M.; Saba, Farrokh 3 1997 Minimality and convexity of dominating and related functions in graphs: A unifying theory. Zbl 0883.05078Cockayne, E. J.; Mynhardt, C. M. 2 1997 Triangle-free graphs with unequal upper domination and irredundance numbers. Zbl 0881.05069Cockayne, E. J.; Mynhardt, C. M. 1 1997 On a generalization of signed dominating functions of graphs. Zbl 0881.05060Cockayne, E. J.; Mynhardt, C. M. 23 1996 Domination critical graphs with higher independent domination numbers. Zbl 0852.05053Ao, S.; Cockayne, E. J.; MacGillivray, G.; Mynhardt, C. M. 7 1996 ...and 39 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 513 Authors 78 Henning, Michael Anthony 42 Mynhardt, Christina Magdalena 27 Haynes, Teresa W. 21 Cockayne, Ernest J. 14 Hedetniemi, Stephen Travis 14 Klostermeyer, William F. 12 Favaron, Odile 12 Yeo, Anders 10 Goddard, Wayne Dean 10 Hattingh, Johannes H. 9 Burger, Alewyn Petrus 9 Jafari Rad, Nader 9 MacGillivray, Gary 9 Southey, Justin 8 Chellali, Mustapha 8 McRae, Alice A. 7 Dettlaff, Magda 7 Lemańska, Magdalena 7 Rautenbach, Dieter 7 Rodríguez-Velazquez, Juan Alberto 7 van der Merwe, Lucas C. 6 Desormeaux, Wyatt J. 6 Pushpam, P. Roushini Leely 6 Yero, Ismael Gonzalez 5 Arumugam, Subramanian 5 Ekim, Tınaz 5 Finbow, Stephen 5 Gimbel, John G. 5 Hedetniemi, Sandra Lee Mitchell 5 Kang, Liying 5 Raczek, Joanna 5 Shan, Erfang 5 Sheikholeslami, Seyed Mahmoud 4 Cabrera Martínez, Abel 4 Chen, Xuegang 4 de Villiers, Anton Pierre 4 Fernau, Henning 4 Kratsch, Dieter 4 Lu, Changhong 4 Mc Inerney, Fionn 4 Messinger, Margaret-Ellen 4 Mondal, Sukumar 4 Nisse, Nicolas 4 Pérennes, Stéphane 4 Sun, Liang 4 Suseendran, Chitra 4 van Vuuren, Jan Harm 4 Volkmann, Lutz 4 Xu, Baogen 4 Xu, Junming 3 Araki, Toru 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 Canoy, Sergio Rosales jun. 3 Chang, Gerard Jennhwa 3 Charon, Irène 3 Cohen, Nathann 3 Dantas, Simone 3 Dorbec, Paul 3 Foucaud, Florent 3 Golovach, Petr A. 3 Grobler, P. J. P. 3 Hartnell, Bert L. 3 Hu, Futao 3 Hudry, Olivier 3 Jha, Anupriya 3 Klavžar, Sandi 3 Laskar, Renu Chakravarti 3 Li, Zepeng 3 Liedloff, Mathieu 3 Lobstein, Antoine-Christophe 3 Lu, You 3 Pal, Madhumangal 3 Puech, Joël 3 Slater, Peter James 3 Wang, Changping 3 Xu, Jin 3 Yi, Eunjeong 3 Zuazua, Rita Esther 3 Żyliński, Paweł 2 Ahangar, Hossein Abdollahzadeh 2 Ait-Ferhat, Dehia 2 Alvarado, José D. 2 Amjadi, Jafar 2 Atapour, Maryam 2 Babu, Jasine 2 Bazgan, Cristina 2 Cáceres, José 2 Casel, Katrin 2 Chen, Lei 2 Corneil, Derek Gordon 2 Divya Rashmi, S. V. 2 Domke, Gayla S. 2 Dunbar, Jean E. 2 Fang, Qizhi ...and 413 more Authors all top 5 Cited in 75 Serials 104 Discrete Mathematics 68 Discrete Applied Mathematics 22 Graphs and Combinatorics 17 Journal of Combinatorial Optimization 15 Discussiones Mathematicae. Graph Theory 14 Discrete Mathematics, Algorithms and Applications 11 Theoretical Computer Science 10 Quaestiones Mathematicae 9 Information Processing Letters 9 Journal of Graph Theory 8 AKCE International Journal of Graphs and Combinatorics 7 The Australasian Journal of Combinatorics 6 Central European Journal of Mathematics 6 Discrete Optimization 5 Czechoslovak Mathematical Journal 5 Journal of Discrete Mathematical Sciences & Cryptography 5 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 Advances and Applications in Discrete Mathematics 3 Algorithmica 3 Applied Mathematics Letters 3 The Electronic Journal of Combinatorics 3 Opuscula Mathematica 3 Journal of Applied Mathematics and Computing 3 Transactions on Combinatorics 3 AIMS Mathematics 2 Journal of Combinatorial Theory. Series B 2 European Journal of Combinatorics 2 Annals of Combinatorics 2 Cryptography and Communications 2 RAIRO. 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DMTCS 1 Wuhan University Journal of Natural Sciences (WUJNS) 1 Discrete Dynamics in Nature and Society 1 Integers 1 Iranian Journal of Science and Technology. Transaction A: Science 1 South East Asian Journal of Mathematics and Mathematical Sciences 1 Journal of Discrete Algorithms 1 Cubo 1 New Mathematics and Natural Computation 1 Mathematics in Computer Science 1 Applicable Analysis and Discrete Mathematics 1 Asian-European Journal of Mathematics 1 Acta Universitatis Sapientiae. Informatica 1 Algorithms 1 International Journal of Combinatorics 1 Journal of Mathematics 1 Electronic Journal of Graph Theory and Applications 1 Journal of Optimization 1 Communications in Combinatorics and Optimization 1 Ural Mathematical Journal 1 DML. Discrete Mathematics Letters all top 5 Cited in 13 Fields 397 Combinatorics (05-XX) 50 Computer science (68-XX) 25 Operations research, mathematical programming (90-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Information and communication theory, circuits (94-XX) 3 Commutative algebra (13-XX) 2 Manifolds and cell complexes (57-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.