On the distance domination number of bipartite graphs

Doost Ali Mojdeh (Department of Mathematics, University of Mazandaran, Babolsar, Iran)
Seyed Reza Musawi (Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 36199-9516, Shahrood, Iran & Department of Mathematics, University of Tafresh, Tafresh, Iran)
Esmaeil Nazari (Department of Mathematics, University of Tafresh, Tafresh, Iran)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 8, No 2 (2020): Electronic Journal of Graph Theory and Applications

‎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 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]‎.