On the distance domination number of bipartite graphs [article]

D. A. Mojdeh, S. R. Musawi, E. Nazari
2018 arXiv   pre-print
A subset D⊆ V(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 bound on the k-distance domination number of a connected bipartite graph and improve some results have been given like Theorem 2.1 and 2,7 in [Tian and Xu, A note on distance domination of graphs, Australian Journal of Combinatorics, 43 (2009), 181-190].
arXiv:1805.01280v1 fatcat:grlhbdsolbczhaqfrrpdxhpwrm