On the distance domination number of bipartite graphs

Doost Ali Mojdeh, Seyed Reza Musawi, Esmaeil Nazari


‎A subset DV(G) is called a k-distance dominating set of G if every vertex in V(G)-D is within distance k from some vertex of D‎. ‎The minimum cardinality among all k-distance dominating sets of G is called the k-distance domination number of G. ‎In this note we give upper bounds on the k-distance domination number of a connected bipartite graph‎, ‎and improve some results have been given like Theorems 2.1 and 2.7 in [Tian and Xu‎, ‎A note on distance domination of graphs‎, ‎Australasian Journal of Combinatorics‎, ‎43 (2009)‎, ‎181-190]‎.



Domination‎, ‎$k$-distance domination‎, ‎connected bipartite

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DOI: http://dx.doi.org/10.5614/ejgta.2020.8.2.11


N. Alon and J.H. Spencer, The Probabilistic Method, 2nd ed. John Willy and Sons, INC. New York, USA, (2000).

I.J. Dejter and O. Serra, Efficient dominating sets in Cayley graphs. Discrete Appl. Math. 129 (2003), 319-328.

A. Hansberg, D. Meierling and L. Volkmann, Distance domination and distance irredundance in graphs, Electron. J. Combin., 14 (2007), R35.

T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of domination in graphs, Marcel Dekker, INC. New York, USA, (1998).

D.A. Mojdeh, A. Sayed-Khalkhali, H. Abdollahzadeh Ahangar and Y. Zhao, Total k-distance domination critical graphs, Transactions on Combinatorics, 5 (3) (2016), 1-9.

J. Raczek, Distance paired domination numbers of graphs, Discrete Math., 308 (2008), 2473- 2483.

F. Tian, J-M. Xu, A note on distance domination of graphs, Australas. J. Combin., 43 (2009) 181-190.

E. Vatandoost, M. Khalili, Domination number of the non-commuting graph of finite groups, Electron. J. Graph Theory Appl. 6 (2) (2018), 228-237.

D.B. West, Introduction to Graph Theory, 2nd ed. Prentice Hall, USA, (2001).


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