Grundy dominating sequences and zero forcing sets

Discrete Optimization - Tập 26 - Trang 66-77 - 2017
Boštjan Brešar1,2, Csilla Bujtás3,4, Tanja Gologranc1,2, Sandi Klavžar5,1,2, Gašper Košmrlj2,6, Balázs Patkós4, Zsolt Tuza3,4, Máté Vizer4
1Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia
2Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia
3Faculty of Information Technology, University of Pannonia, Veszprém, Hungary
4Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary
5Faculty of Mathematics and Physics, University of Ljubljana, Slovenia
6Abelium R&D, Ljubljana, Slovenia

Tài liệu tham khảo

Brešar, 2014, Dominating sequences in graphs, Discrete Math., 336, 22, 10.1016/j.disc.2014.07.016 Brešar, 2016, Dominating sequences under atomic changes with applications in Sierpiński and interval graphs, Appl. Anal. Discrete Math., 10, 518, 10.2298/AADM161005024B Brešar, 2016, Dominating sequences in grid-like and toroidal graphs, Electron. J. Combin., 23, 19, 10.37236/6269 Brešar, 2016, Total dominating sequences in graphs, Discrete Math., 339, 1665, 10.1016/j.disc.2016.01.017 2008, Zero forcing sets and the minimum rank of graphs, Linear Algebra Appl., 428, 1628, 10.1016/j.laa.2007.10.009 K.F. Benson, D. Ferrero, M. Flagg, V. Furst, L. Hogben, V. Vasilevskak, B. Wissman, Power domination and zero forcing, arXiv:1510.02421 [math.CO]. Haynes, 2002, Domination in graphs applied to electric power networks, SIAM J. Discrete Math., 15, 519, 10.1137/S0895480100375831 Aazami, 2008 Barioli, 2010, Zero forcing parameters and minimum rank problems, Linear Algebra Appl., 433, 401, 10.1016/j.laa.2010.03.008 Huang, 2010, On minimum rank and zero forcing sets of a graph, Linear Algebra Appl., 432, 2961, 10.1016/j.laa.2010.01.001 Taklimi, 2014, On the relationships between zero forcing numbers and certain graph coverings, Spec. Matrices, 2, 30 Hammack, 2011 Klavžar, 1997, Graphs S(n,k) and a variant of the Tower of Hanoi problem, Czechoslovak Math. J., 47, 95, 10.1023/A:1022444205860 Hinz, 2017, A survey and classification of Sierpiński-type graphs, Discrete Appl. Math., 217, 565, 10.1016/j.dam.2016.09.024 B. Brešar, T. Kos, G. Nasini, P. Torres, Total dominating sequences in trees, split graphs, and under modular decomposition, arXiv:1608.06804 [math.CO]. Chang, 2012, Generalized power domination of graphs, Discrete Appl. Math., 160, 1691, 10.1016/j.dam.2012.03.007 Amos, 2015, Upper bounds on the k-forcing number of a graph, Discrete Appl. Math., 181, 1, 10.1016/j.dam.2014.08.029 D. Ferrero, L. Hogben, F.H.J. Kenter, M. Young, The relationship between k-forcing and k-power domination, arXiv:1701.08386 [math.CO]. Fink, 1985, On n-domination, n-dependence and forbidden subgraphs, 301 Argiroffo, 2015, On the complexity of {k}-domination and k-tuple domination in graphs, Inform. Process. Lett., 115, 556, 10.1016/j.ipl.2015.01.007 Hansberg, 2009, Upper bounds on the k-domination number and the k-Roman domination number, Discrete Appl. Math., 157, 1634, 10.1016/j.dam.2008.10.011 Chellali, 2012, k-domination and k-independence in graphs: a survey, Graphs Combin., 28, 1, 10.1007/s00373-011-1040-3 Hogben, 2012, Propagation time for zero forcing on a graph, Discrete Appl. Math., 160, 1994, 10.1016/j.dam.2012.04.003 Aazami, 2010, Domination in graphs with bounded propagation: algorithms, formulations and hardness results, J. Comb. Optim., 19, 429, 10.1007/s10878-008-9176-7 Dorbec, 2014, Generalized power domination: propagation radius and Sierpiński graphs, Acta Appl. Math., 134, 75, 10.1007/s10440-014-9870-7 Liao, 2016, Power domination with bounded time constraints, J. Comb. Optim., 31, 725, 10.1007/s10878-014-9785-2