Edit Profile (opens in new tab) Rall, Douglas F. Compute Distance To: Compute Author ID: rall.douglas-f Published as: Rall, Douglas F.; Rall, Douglas; Rall, D. F.; Rall, D.; Rall, Doug F.; Rall, Doug more...less Homepage: http://math.furman.edu/~drall/ External Links: MGP Documents Indexed: 101 Publications since 1979, including 2 Books Co-Authors: 48 Co-Authors with 94 Joint Publications 1,492 Co-Co-Authors all top 5 Co-Authors 7 single-authored 30 Hartnell, Bert L. 24 Brešar, Boštjan 24 Klavžar, Sandi 18 Henning, Michael Anthony 8 Gunther, Georg 7 Hedetniemi, Stephen Travis 6 Hedetniemi, Sandra Lee Mitchell 6 Wash, Kirsti 4 Kuenzel, Kirsti 3 Gallant, Robert P. 3 Goddard, Wayne Dean 3 Imrich, Wilfried 3 Markus, Lisa R. 3 Slater, Peter James 3 Šumenjak, Tadeja Kraner 3 Horvat, Aleksandra Tepeh 2 Anderson, Sarah E. 2 Dorbec, Paul 2 Dunbar, Jean E. 2 Finbow, Arthur S. 2 Knisely, James A. 2 Košmrlj, Gašper 2 Nowakowski, Richard Joseph 1 Blair, Jean R. S. 1 Brigham, Robert C. 1 Brown, Jason Ira 1 Desormeaux, Wyatt J. 1 Dow, Stephen J. 1 Dravec, Tanja 1 Favaron, Odile 1 Ferme, Jasmina 1 Harris, John M. 1 Haynes, Teresa W. 1 Jacobson, Michael Scott 1 Jamison, Robert E. 1 Jerebic, Janja 1 Laskar, Renu Chakravarti 1 Manne, Fredrik 1 Martin, Scott P. 1 Milanič, Martin 1 Peterin, Iztok 1 Peters, Kenneth 1 Peyrat, Claudine 1 Powell, Jeffrey Scott 1 Rizzi, Romeo 1 Whitehead, Carol A. 1 Yeo, Anders 1 Yero, Ismael Gonzalez all top 5 Serials 14 Discrete Mathematics 9 Discrete Applied Mathematics 9 Graphs and Combinatorics 9 Discussiones Mathematicae. Graph Theory 7 Congressus Numerantium 5 Ars Combinatoria 4 Journal of Graph Theory 4 JCMCC. The Journal of Combinatorial Mathematics and Combinatorial Computing 3 Discrete Mathematics and Theoretical Computer Science. DMTCS 3 Ars Mathematica Contemporanea 2 Czechoslovak Mathematical Journal 2 SIAM Journal on Discrete Mathematics 2 Aequationes Mathematicae 2 The Australasian Journal of Combinatorics 1 Applied Mathematics and Computation 1 International Journal of Mathematics and Mathematical Sciences 1 Networks 1 Utilitas Mathematica 1 European Journal of Combinatorics 1 Combinatorica 1 Bulletin of the Institute of Combinatorics and its Applications 1 The Electronic Journal of Combinatorics 1 Taiwanese Journal of Mathematics 1 Journal of Combinatorial Optimization 1 Annals of Combinatorics 1 AKCE International Journal of Graphs and Combinatorics 1 SpringerBriefs in Mathematics 1 Indian Journal of Discrete Mathematics Fields 99 Combinatorics (05-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Computer science (68-XX) 1 Associative rings and algebras (16-XX) 1 Operations research, mathematical programming (90-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 87 Publications have been cited 1,149 times in 625 Documents Cited by ▼ Year ▼ Rainbow domination in graphs. Zbl 1163.05046Brešar, Boštjan; Henning, Michael A.; Rall, Douglas F. 77 2008 Domination game and an imagination strategy. Zbl 1223.05189Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F. 72 2010 Broadcast chromatic numbers of graphs. Zbl 1224.05172Goddard, Wayne; Hedetniemi, Sandra M.; Hedetniemi, Stephen T.; Harris, John M.; Rall, Douglas F. 59 2008 Topics in graph theory. Graphs and their Cartesian product. Zbl 1156.05001Imrich, Wilfried; Klavžar, Sandi; Rall, Douglas F. 49 2008 Total version of the domination game. Zbl 1321.05159Henning, Michael A.; Klavžar, Sandi; Rall, Douglas F. 43 2015 On the packing chromatic number of Cartesian products, hexagonal lattice, and trees. Zbl 1126.05045Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F. 41 2007 Vizing’s conjecture: a survey and recent results. Zbl 1234.05173Brešar, Boštjan; Dorbec, Paul; Goddard, Wayne; Hartnell, Bert L.; Henning, Michael A.; Klavžar, Sandi; Rall, Douglas F. 41 2012 Bounds on the bondage number of a graph. Zbl 0796.05051Hartnell, Bert L.; Rall, Douglas F. 37 1994 Associative graph products and their independence, domination and coloring numbers. Zbl 0865.05071Nowakowski, Richard J.; Rall, Douglas F. 34 1996 Distance-balanced graphs. Zbl 1154.05026Jerebic, Janja; Klavžar, Sandi; Rall, Douglas F. 31 2008 On dominating the Cartesian product of a graph and \(K_2\). Zbl 1063.05107Hartnell, Bert L.; Rall, Douglas F. 30 2004 On the packing chromatic number of some lattices. Zbl 1221.05137Finbow, Arthur S.; Rall, Douglas F. 30 2010 Domination game played on trees and spanning subgraphs. Zbl 1262.05104Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F. 28 2013 Domination game: extremal families of graphs for \(3/5\)-conjectures. Zbl 1287.05088Brešar, Boštjan; Klavžar, Sandi; Košmrlj, Gašper; Rall, Douglas F. 26 2013 Domination in Cartesian products: Vizing’s conjecture. Zbl 0890.05035Hartnell, Bert; Rall, Douglas F. 24 1998 Rainbow domination in the lexicographic product of graphs. Zbl 1286.05146Šumenjak, Tadeja Kraner; Rall, Douglas F.; Tepeh, Aleksandra 23 2013 The 4/5 upper bound on the game total domination number. Zbl 1399.05165Henning, Michael A.; Klavžar, Sandi; Rall, Douglas F. 23 2017 Limited packings in graphs. Zbl 1218.05132Gallant, Robert; Gunther, Georg; Hartnell, Bert L.; Rall, Douglas F. 22 2010 Dominating sequences in graphs. Zbl 1300.05210Brešar, Boštjan; Gologranc, Tanja; Milanič, Martin; Rall, Douglas F.; Rizzi, Romeo 19 2014 Total dominating sequences in graphs. Zbl 1333.05214Brešar, Boštjan; Henning, Michael A.; Rall, Douglas F. 19 2016 Packing chromatic number under local changes in a graph. Zbl 1357.05037Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F.; Wash, Kirsti 19 2017 Packing chromatic number of base-3 Sierpiński graphs. Zbl 1342.05111Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F. 18 2016 A characterization of trees in which no edge is essential to the domination number. Zbl 0767.05078Hartnell, Bert L.; Rall, Douglas F. 18 1992 Progress towards the total domination game \(\frac{3}{4}\)-conjecture. Zbl 1339.05255Henning, Michael A.; Rall, Douglas F. 17 2016 On the total domination number of Cartesian products of graphs. Zbl 1062.05109Henning, Michael A.; Rall, Douglas F. 17 2005 Packing chromatic number, \((1, 1, 2, 2)\)-colorings, and characterizing the Petersen graph. Zbl 1355.05194Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F.; Wash, Kirsti 16 2017 Total domination in categorical products of graphs. Zbl 1074.05068Rall, Douglas F. 16 2005 Trees with equal total domination and game total domination numbers. Zbl 1365.05199Henning, Michael A.; Rall, Douglas F. 15 2017 Paired-domination of Cartesian products of graphs and rainbow domination. Zbl 1200.05154Brešar, Boštjan; Henning, Michael A.; Rall, Douglas F. 14 2005 Graphs with unique minimum dominating sets. Zbl 0836.05045Gunther, G.; Hartnell, B.; Markus, L. R.; Rall, D. 13 1994 Paired-domination of Cartesian products of graphs. Zbl 1161.05053Brešar, Boštjan; Henning, Michael A.; Rall, Douglas F. 13 2007 On location-domination numbers for certain classes of graphs. Zbl 0568.05033Rall, Douglas F.; Slater, Peter J. 12 1984 Dominating direct products of graphs. Zbl 1116.05055Brešar, Bostjan; Klavžar, Sandi; Rall, Douglas F. 12 2007 Game total domination critical graphs. Zbl 1398.05135Henning, Michael A.; Klavžar, Sandi; Rall, Douglas F. 12 2018 Fall colorings of graphs. Zbl 0962.05020Dunbar, J. E.; Hedetniemi, S. M.; Hedetniemi, S. T.; Jacobs, D. P.; Knisely, J.; Laskar, R. C.; Rall, D. F. 11 2000 Bicritical domination. Zbl 1078.05062Brigham, Robert C.; Haynes, Teresa W.; Henning, Michael A.; Rall, Douglas F. 10 2005 A characterization of graphs in which some minimum dominating set covers all the edges. Zbl 0836.05065Hartnell, Bert; Rall, Douglas F. 9 1995 Domination game and minimal edge cuts. Zbl 1405.05115Klavžar, Sandi; Rall, Douglas F. 9 2019 On iterated clique graphs with increasing diameters. Zbl 0596.05036Peyrat, C.; Rall, D. F.; Slater, P. J. 8 1986 Graphs whose vertex independence number is unaffected by single edge addition or deletion. Zbl 0792.05116Gunther, Georg; Hartnell, Bert; Rall, Douglas F. 8 1993 Acyclic domination. Zbl 0961.05052Hedetniemi, S. M.; Hedetniemi, S. T.; Rall, D. F. 8 2000 Packing chromatic number versus chromatic and clique number. Zbl 1390.05186Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F.; Wash, Kirsti 8 2018 Vizing’s conjecture and the one-half argument. Zbl 0845.05074Hartnell, Bert; Rall, Douglas F. 7 1995 On Vizing’s conjecture. Zbl 0764.05092Hartnell, Bert L.; Rall, Douglas F. 7 1991 Relating the annihilation number and the 2-domination number of a tree. Zbl 1281.05104Desormeaux, Wyatt J.; Henning, Michael A.; Rall, Douglas F.; Yeo, Anders 7 2014 Identifying codes of the direct product of two cliques. Zbl 1284.05200Rall, Douglas F.; Wash, Kirsti 7 2014 On the upper total domination number of Cartesian products of graphs. Zbl 1157.05042Dorbec, Paul; Henning, Michael A.; Rall, Douglas F. 6 2008 On \(k\)-dependent domination. Zbl 0994.05108Favaron, O.; Hedetniemi, S. M.; Hedetniemi, S. T.; Rall, D. F. 6 2002 A bound on the size of a graph with given order and bondage number. Zbl 0960.05074Hartnell, Bert L.; Rall, Douglas F. 6 1999 On the independence number of the Cartesian product of caterpillars. Zbl 1071.05554Martin, Scott P.; Powell, Jeffrey S.; Rall, Douglas F. 6 2001 On graphs with disjoint dominating and 2-dominating sets. Zbl 1291.05144Henning, Michael A.; Rall, Douglas F. 6 2013 On \(n\)-irredundance and \(n\)-domination. Zbl 0743.05063Jacobson, Michael S.; Peters, Kenneth; Rall, Douglas F. 5 1990 Fair reception and Vizing’s conjecture. Zbl 1179.05080Brešar, Boštjan; Rall, Douglas F. 5 2009 Secondary domination in graphs. Zbl 1176.05055Hedetniemi, Sandra M.; Hedetniemi, Stephen T.; Knisely, James; Rall, Douglas F. 5 2008 The ultimate categorical independence ratio of a graph. Zbl 0848.05036Brown, Jason I.; Nowakowski, Richard J.; Rall, Douglas 4 1996 Domatically critical and domatically full graphs. Zbl 0745.05061Rall, Douglas F. 4 1990 On the Cartesian product of non well-covered graphs. Zbl 1266.05133Hartnell, Bert L.; Rall, Douglas F. 4 2013 Limited packings in graphs. Zbl 1341.05208Gallant, Robert; Gunther, Georg; Hartnell, Bert; Rall, Douglas 4 2008 On \(k\)-rainbow independent domination in graphs. Zbl 1427.05162Kraner Šumenjak, Tadeja; Rall, Douglas F.; Tepeh, Aleksandra 4 2018 Connected domatic number in planar graphs. Zbl 1079.05512Hartnell, Bert L.; Rall, Douglas F. 3 2001 Partitioning the vertex set of \(G\) to make \(G\square H\) an efficient open domination graph. Zbl 1400.05204Šumenjak, Tadeja Kraner; Peterin, Iztok; Rall, Douglas F.; Tepeh, Aleksandra 3 2016 On minimum identifying codes in some Cartesian product graphs. Zbl 1371.05220Rall, Doug F.; Wash, K. 3 2017 Packing chromatic vertex-critical graphs. Zbl 1411.05091Klavžar, Sandi; Rall, Douglas F. 3 2019 Cancellation properties of products of graphs. Zbl 1126.05071Imrich, Wilfried; Klavžar, Sandi; Rall, Douglas F. 2 2007 The watchman’s walk problem: An introduction. Zbl 0952.05053Hartnell, B. L.; Rall, D. F.; Whitehead, C. A. 2 1998 On graphs in which every minimal total dominating set is minimum. Zbl 0899.05030Hartnell, Bert; Rall, Douglas F. 2 1997 On graphs having maximal independent sets of exactly \(t\) distinct cardinalities. Zbl 1267.05189Hartnell, Bert L.; Rall, Douglas F. 2 2013 Domination games played on graphs. Zbl 1467.91015Brešar, Boštjan; Henning, Michael A.; Klavžar, Sandi; Rall, Douglas F. 2 2021 Uniformly dissociated graphs. Zbl 1380.05148Brešar, Boštjan; Hartnell, Bert L.; Rall, Douglas F. 2 2017 Guarded subgraphs and the domination game. Zbl 1311.05123Brešar, Boštjan; Klavžar, Sandi; Košmrlj, Gasper; Rall, Doug F. 2 2015 On well-covered Cartesian products. Zbl 1441.05197Hartnell, Bert L.; Rall, Douglas F.; Wash, Kirsti 2 2018 A survey on packing colorings. Zbl 1446.05031Brešar, Boštjan; Ferme, Jasmina; Klavžar, Sandi; Rall, Douglas F. 2 2020 Star-factors and \(k\)-bounded total domination. Zbl 0854.05088Gunther, Georg; Hartnell, Bert; Rall, Douglas 1 1996 Dominating a graph and its complement. Zbl 0728.05054Rall, Douglas F. 1 1991 On Cartesian products having a minimum dominating set that is a box or a stairway. Zbl 1327.05255Brešar, Boštjan; Rall, Douglas F. 1 2015 On graphs having uniform size star factors. Zbl 1109.05084Hartnell, Bert L.; Rall, Douglas F. 1 2006 Lower bounds for dominating Cartesian products. Zbl 0938.05048Hartnell, Bert L.; Rall, Douglas F. 1 1999 A class of rings which are algebraic over the integers. Zbl 0425.16021Rall, Douglas F. 1 1979 A fractional version of domatic number. Zbl 0691.05044Rall, Douglas F. 1 1990 Finite and infinite hypercubes as direct products. Zbl 1115.05074Imrich, Wilfried; Rall, Douglas 1 2006 A game of edge removal on graphs. Zbl 1187.91030Gallant, Robert P.; Gunther, Georg; Hartnell, Bert L.; Rall, Douglas F. 1 2006 A vertex-magic edge labeling game. Zbl 1045.05079Hartnell, B.; Rall, D. 1 2003 Improving some bounds for dominating Cartesian products. Zbl 1055.05115Hartnell, Bert L.; Rall, Douglas F. 1 2003 On the packing chromatic number of Cartesian products, hexagonal lattice, and trees. Zbl 1341.05064Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F. 1 2007 On the packing chromatic number of trees, Cartesian products and some infinite graphs. Zbl 1341.05089Rall, Douglas F.; Brešar, Boštjan; Finbow, Arthur S.; Klavžar, Sandi 1 2008 Packing and domination invariants on Cartesian products and direct products. Zbl 1168.05353Rall, Douglas F. 1 2008 A new framework to approach Vizing’s conjecture. Zbl 1459.05231Brešar, Boštjan; Hartnell, Bert L.; Henning, Michael A.; Kuenzel, Kirsti; Rall, Douglas F. 1 2021 Domination games played on graphs. Zbl 1467.91015Brešar, Boštjan; Henning, Michael A.; Klavžar, Sandi; Rall, Douglas F. 2 2021 A new framework to approach Vizing’s conjecture. Zbl 1459.05231Brešar, Boštjan; Hartnell, Bert L.; Henning, Michael A.; Kuenzel, Kirsti; Rall, Douglas F. 1 2021 A survey on packing colorings. Zbl 1446.05031Brešar, Boštjan; Ferme, Jasmina; Klavžar, Sandi; Rall, Douglas F. 2 2020 Domination game and minimal edge cuts. Zbl 1405.05115Klavžar, Sandi; Rall, Douglas F. 9 2019 Packing chromatic vertex-critical graphs. Zbl 1411.05091Klavžar, Sandi; Rall, Douglas F. 3 2019 Game total domination critical graphs. Zbl 1398.05135Henning, Michael A.; Klavžar, Sandi; Rall, Douglas F. 12 2018 Packing chromatic number versus chromatic and clique number. Zbl 1390.05186Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F.; Wash, Kirsti 8 2018 On \(k\)-rainbow independent domination in graphs. Zbl 1427.05162Kraner Šumenjak, Tadeja; Rall, Douglas F.; Tepeh, Aleksandra 4 2018 On well-covered Cartesian products. Zbl 1441.05197Hartnell, Bert L.; Rall, Douglas F.; Wash, Kirsti 2 2018 The 4/5 upper bound on the game total domination number. Zbl 1399.05165Henning, Michael A.; Klavžar, Sandi; Rall, Douglas F. 23 2017 Packing chromatic number under local changes in a graph. Zbl 1357.05037Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F.; Wash, Kirsti 19 2017 Packing chromatic number, \((1, 1, 2, 2)\)-colorings, and characterizing the Petersen graph. Zbl 1355.05194Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F.; Wash, Kirsti 16 2017 Trees with equal total domination and game total domination numbers. Zbl 1365.05199Henning, Michael A.; Rall, Douglas F. 15 2017 On minimum identifying codes in some Cartesian product graphs. Zbl 1371.05220Rall, Doug F.; Wash, K. 3 2017 Uniformly dissociated graphs. Zbl 1380.05148Brešar, Boštjan; Hartnell, Bert L.; Rall, Douglas F. 2 2017 Total dominating sequences in graphs. Zbl 1333.05214Brešar, Boštjan; Henning, Michael A.; Rall, Douglas F. 19 2016 Packing chromatic number of base-3 Sierpiński graphs. Zbl 1342.05111Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F. 18 2016 Progress towards the total domination game \(\frac{3}{4}\)-conjecture. Zbl 1339.05255Henning, Michael A.; Rall, Douglas F. 17 2016 Partitioning the vertex set of \(G\) to make \(G\square H\) an efficient open domination graph. Zbl 1400.05204Šumenjak, Tadeja Kraner; Peterin, Iztok; Rall, Douglas F.; Tepeh, Aleksandra 3 2016 Total version of the domination game. Zbl 1321.05159Henning, Michael A.; Klavžar, Sandi; Rall, Douglas F. 43 2015 Guarded subgraphs and the domination game. Zbl 1311.05123Brešar, Boštjan; Klavžar, Sandi; Košmrlj, Gasper; Rall, Doug F. 2 2015 On Cartesian products having a minimum dominating set that is a box or a stairway. Zbl 1327.05255Brešar, Boštjan; Rall, Douglas F. 1 2015 Dominating sequences in graphs. Zbl 1300.05210Brešar, Boštjan; Gologranc, Tanja; Milanič, Martin; Rall, Douglas F.; Rizzi, Romeo 19 2014 Relating the annihilation number and the 2-domination number of a tree. Zbl 1281.05104Desormeaux, Wyatt J.; Henning, Michael A.; Rall, Douglas F.; Yeo, Anders 7 2014 Identifying codes of the direct product of two cliques. Zbl 1284.05200Rall, Douglas F.; Wash, Kirsti 7 2014 Domination game played on trees and spanning subgraphs. Zbl 1262.05104Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F. 28 2013 Domination game: extremal families of graphs for \(3/5\)-conjectures. Zbl 1287.05088Brešar, Boštjan; Klavžar, Sandi; Košmrlj, Gašper; Rall, Douglas F. 26 2013 Rainbow domination in the lexicographic product of graphs. Zbl 1286.05146Šumenjak, Tadeja Kraner; Rall, Douglas F.; Tepeh, Aleksandra 23 2013 On graphs with disjoint dominating and 2-dominating sets. Zbl 1291.05144Henning, Michael A.; Rall, Douglas F. 6 2013 On the Cartesian product of non well-covered graphs. Zbl 1266.05133Hartnell, Bert L.; Rall, Douglas F. 4 2013 On graphs having maximal independent sets of exactly \(t\) distinct cardinalities. Zbl 1267.05189Hartnell, Bert L.; Rall, Douglas F. 2 2013 Vizing’s conjecture: a survey and recent results. Zbl 1234.05173Brešar, Boštjan; Dorbec, Paul; Goddard, Wayne; Hartnell, Bert L.; Henning, Michael A.; Klavžar, Sandi; Rall, Douglas F. 41 2012 Domination game and an imagination strategy. Zbl 1223.05189Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F. 72 2010 On the packing chromatic number of some lattices. Zbl 1221.05137Finbow, Arthur S.; Rall, Douglas F. 30 2010 Limited packings in graphs. Zbl 1218.05132Gallant, Robert; Gunther, Georg; Hartnell, Bert L.; Rall, Douglas F. 22 2010 Fair reception and Vizing’s conjecture. Zbl 1179.05080Brešar, Boštjan; Rall, Douglas F. 5 2009 Rainbow domination in graphs. Zbl 1163.05046Brešar, Boštjan; Henning, Michael A.; Rall, Douglas F. 77 2008 Broadcast chromatic numbers of graphs. Zbl 1224.05172Goddard, Wayne; Hedetniemi, Sandra M.; Hedetniemi, Stephen T.; Harris, John M.; Rall, Douglas F. 59 2008 Topics in graph theory. Graphs and their Cartesian product. Zbl 1156.05001Imrich, Wilfried; Klavžar, Sandi; Rall, Douglas F. 49 2008 Distance-balanced graphs. Zbl 1154.05026Jerebic, Janja; Klavžar, Sandi; Rall, Douglas F. 31 2008 On the upper total domination number of Cartesian products of graphs. Zbl 1157.05042Dorbec, Paul; Henning, Michael A.; Rall, Douglas F. 6 2008 Secondary domination in graphs. Zbl 1176.05055Hedetniemi, Sandra M.; Hedetniemi, Stephen T.; Knisely, James; Rall, Douglas F. 5 2008 Limited packings in graphs. Zbl 1341.05208Gallant, Robert; Gunther, Georg; Hartnell, Bert; Rall, Douglas 4 2008 On the packing chromatic number of trees, Cartesian products and some infinite graphs. Zbl 1341.05089Rall, Douglas F.; Brešar, Boštjan; Finbow, Arthur S.; Klavžar, Sandi 1 2008 Packing and domination invariants on Cartesian products and direct products. Zbl 1168.05353Rall, Douglas F. 1 2008 On the packing chromatic number of Cartesian products, hexagonal lattice, and trees. Zbl 1126.05045Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F. 41 2007 Paired-domination of Cartesian products of graphs. Zbl 1161.05053Brešar, Boštjan; Henning, Michael A.; Rall, Douglas F. 13 2007 Dominating direct products of graphs. Zbl 1116.05055Brešar, Bostjan; Klavžar, Sandi; Rall, Douglas F. 12 2007 Cancellation properties of products of graphs. Zbl 1126.05071Imrich, Wilfried; Klavžar, Sandi; Rall, Douglas F. 2 2007 On the packing chromatic number of Cartesian products, hexagonal lattice, and trees. Zbl 1341.05064Brešar, Boštjan; Klavžar, Sandi; Rall, Douglas F. 1 2007 On graphs having uniform size star factors. Zbl 1109.05084Hartnell, Bert L.; Rall, Douglas F. 1 2006 Finite and infinite hypercubes as direct products. Zbl 1115.05074Imrich, Wilfried; Rall, Douglas 1 2006 A game of edge removal on graphs. Zbl 1187.91030Gallant, Robert P.; Gunther, Georg; Hartnell, Bert L.; Rall, Douglas F. 1 2006 On the total domination number of Cartesian products of graphs. Zbl 1062.05109Henning, Michael A.; Rall, Douglas F. 17 2005 Total domination in categorical products of graphs. Zbl 1074.05068Rall, Douglas F. 16 2005 Paired-domination of Cartesian products of graphs and rainbow domination. Zbl 1200.05154Brešar, Boštjan; Henning, Michael A.; Rall, Douglas F. 14 2005 Bicritical domination. Zbl 1078.05062Brigham, Robert C.; Haynes, Teresa W.; Henning, Michael A.; Rall, Douglas F. 10 2005 On dominating the Cartesian product of a graph and \(K_2\). Zbl 1063.05107Hartnell, Bert L.; Rall, Douglas F. 30 2004 A vertex-magic edge labeling game. Zbl 1045.05079Hartnell, B.; Rall, D. 1 2003 Improving some bounds for dominating Cartesian products. Zbl 1055.05115Hartnell, Bert L.; Rall, Douglas F. 1 2003 On \(k\)-dependent domination. Zbl 0994.05108Favaron, O.; Hedetniemi, S. M.; Hedetniemi, S. T.; Rall, D. F. 6 2002 On the independence number of the Cartesian product of caterpillars. Zbl 1071.05554Martin, Scott P.; Powell, Jeffrey S.; Rall, Douglas F. 6 2001 Connected domatic number in planar graphs. Zbl 1079.05512Hartnell, Bert L.; Rall, Douglas F. 3 2001 Fall colorings of graphs. Zbl 0962.05020Dunbar, J. E.; Hedetniemi, S. M.; Hedetniemi, S. T.; Jacobs, D. P.; Knisely, J.; Laskar, R. C.; Rall, D. F. 11 2000 Acyclic domination. Zbl 0961.05052Hedetniemi, S. M.; Hedetniemi, S. T.; Rall, D. F. 8 2000 A bound on the size of a graph with given order and bondage number. Zbl 0960.05074Hartnell, Bert L.; Rall, Douglas F. 6 1999 Lower bounds for dominating Cartesian products. Zbl 0938.05048Hartnell, Bert L.; Rall, Douglas F. 1 1999 Domination in Cartesian products: Vizing’s conjecture. Zbl 0890.05035Hartnell, Bert; Rall, Douglas F. 24 1998 The watchman’s walk problem: An introduction. Zbl 0952.05053Hartnell, B. L.; Rall, D. F.; Whitehead, C. A. 2 1998 On graphs in which every minimal total dominating set is minimum. Zbl 0899.05030Hartnell, Bert; Rall, Douglas F. 2 1997 Associative graph products and their independence, domination and coloring numbers. Zbl 0865.05071Nowakowski, Richard J.; Rall, Douglas F. 34 1996 The ultimate categorical independence ratio of a graph. Zbl 0848.05036Brown, Jason I.; Nowakowski, Richard J.; Rall, Douglas 4 1996 Star-factors and \(k\)-bounded total domination. Zbl 0854.05088Gunther, Georg; Hartnell, Bert; Rall, Douglas 1 1996 A characterization of graphs in which some minimum dominating set covers all the edges. Zbl 0836.05065Hartnell, Bert; Rall, Douglas F. 9 1995 Vizing’s conjecture and the one-half argument. Zbl 0845.05074Hartnell, Bert; Rall, Douglas F. 7 1995 Bounds on the bondage number of a graph. Zbl 0796.05051Hartnell, Bert L.; Rall, Douglas F. 37 1994 Graphs with unique minimum dominating sets. Zbl 0836.05045Gunther, G.; Hartnell, B.; Markus, L. R.; Rall, D. 13 1994 Graphs whose vertex independence number is unaffected by single edge addition or deletion. Zbl 0792.05116Gunther, Georg; Hartnell, Bert; Rall, Douglas F. 8 1993 A characterization of trees in which no edge is essential to the domination number. Zbl 0767.05078Hartnell, Bert L.; Rall, Douglas F. 18 1992 On Vizing’s conjecture. Zbl 0764.05092Hartnell, Bert L.; Rall, Douglas F. 7 1991 Dominating a graph and its complement. Zbl 0728.05054Rall, Douglas F. 1 1991 On \(n\)-irredundance and \(n\)-domination. Zbl 0743.05063Jacobson, Michael S.; Peters, Kenneth; Rall, Douglas F. 5 1990 Domatically critical and domatically full graphs. Zbl 0745.05061Rall, Douglas F. 4 1990 A fractional version of domatic number. Zbl 0691.05044Rall, Douglas F. 1 1990 On iterated clique graphs with increasing diameters. Zbl 0596.05036Peyrat, C.; Rall, D. F.; Slater, P. J. 8 1986 On location-domination numbers for certain classes of graphs. Zbl 0568.05033Rall, Douglas F.; Slater, Peter J. 12 1984 A class of rings which are algebraic over the integers. Zbl 0425.16021Rall, Douglas F. 1 1979 all cited Publications top 5 cited Publications all top 5 Cited by 721 Authors 66 Klavžar, Sandi 49 Henning, Michael Anthony 46 Brešar, Boštjan 35 Rall, Douglas F. 27 Bujtás, Csilla 18 Volkmann, Lutz 15 Sheikholeslami, Seyed Mahmoud 15 Yero, Ismael Gonzalez 14 Jafari Rad, Nader 14 Tuza, Zsolt 13 Iršič, Vesna 11 Košmrlj, Gašper 11 Mojdeh, Doost Ali 11 Rodríguez-Velazquez, Juan Alberto 10 Dorbec, Paul 10 Peterin, Iztok 9 Leoni, Valeria Alejandra 9 Samadi, Babak 8 Chellali, Mustapha 8 Furuya, Michitaka 8 Hartnell, Bert L. 8 Lemańska, Magdalena 8 Nasini, Graciela L. 8 Shao, Zehui 8 Togni, Olivier 8 Xu, Junming 7 Cabrera Martínez, Abel 7 Dobson, Maria Patricia 7 Dravec, Tanja 7 Gastineau, Nicolas 7 Goddard, Wayne Dean 7 Haynes, Teresa W. 7 Topp, Jerzy 7 Xu, Kexiang 6 Ahangar, Hossein Abdollahzadeh 6 Amjadi, Jafar 6 Dettlaff, Magda 6 Ferme, Jasmina 6 Hedetniemi, Stephen Travis 6 Jakovac, Marko 6 Krzywkowski, Marcin 6 Patkós, Balázs 6 Rautenbach, Dieter 6 Šumenjak, Tadeja Kraner 6 Torres, Pablo Daniel 6 Wash, Kirsti 6 Żyliński, Paweł 5 Fujita, Shinya 5 Gledel, Valentin 5 Hu, Futao 5 Kos, Tim 5 Li, Zepeng 5 Miklavič, Štefko 5 Miotk, Mateusz 5 Raczek, Joanna 5 Horvat, Aleksandra Tepeh 5 Vesel, Aleksander 5 Vijayakumar, Ambat 5 Vizer, Máté 5 Worawannotai, Chalermpong 4 Balakrishnan, Kannan 4 Dehgardi, Nasrin 4 Hao, Guoliang 4 Hinrichsen, Erica G. 4 Holub, Přemysl 4 Hooshmandasl, Mohammad Reza 4 Huang, Jia 4 Hujdurović, Ademir 4 Kang, Liying 4 Klostermeyer, William F. 4 Krop, Elliot 4 Kuenzel, Kirsti 4 Levit, Vadim E. 4 Liu, Xujun 4 Magnant, Colton 4 Meybodi, Mohsen Alambardar 4 Milanič, Martin 4 Mynhardt, Christina Magdalena 4 Rus, Gregor 4 Shan, Erfang 4 Šparl, Primož 4 Wang, Yue-Li 4 Yi, Eunjeong 4 Zhao, Weisheng 3 Anderson, Sarah E. 3 Argiroffo, Gabriela R. 3 Asgharsharghi, Leila 3 Ashrafi, Ali Reza 3 Bermudo, Sergio 3 Bonomo-Braberman, Flavia 3 Borowiecki, Mieczysław 3 Brigham, Robert C. 3 Changat, Manoj 3 Chithra, M. R. 3 Deng, Kecai 3 Dutton, Ronald D. 3 Fiala, Jiří 3 Finbow, Arthur S. 3 Fischermann, Miranca 3 Gözüpek, Didem ...and 621 more Authors all top 5 Cited in 97 Serials 127 Discrete Applied Mathematics 86 Discrete Mathematics 41 Graphs and Combinatorics 33 Discussiones Mathematicae. Graph Theory 30 Journal of Combinatorial Optimization 17 Discrete Mathematics, Algorithms and Applications 16 Applied Mathematics and Computation 13 Theoretical Computer Science 13 The Electronic Journal of Combinatorics 13 Bulletin of the Malaysian Mathematical Sciences Society. 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Discrete Mathematics Letters all top 5 Cited in 19 Fields 602 Combinatorics (05-XX) 66 Computer science (68-XX) 59 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 29 Operations research, mathematical programming (90-XX) 12 Information and communication theory, circuits (94-XX) 9 Biology and other natural sciences (92-XX) 6 Number theory (11-XX) 2 General and overarching topics; collections (00-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Numerical analysis (65-XX) 1 Mathematics education (97-XX) Citations by Year