Lower and upper bounds of 2- domination number for m=6,7 and arbitrary n


Abstract in English

Let be a graph of order n. with vertices and edges . A set D of vertices of a graph is called 2- dominating if every vertex has at least two neighbors in D. let denotes The 2- domination number of a graph G, , is the order of a smallest 2- dominating set of G. In this paper, we found lower and upper bounds of 2- domination number of the cartesian product of two paths for m=6,7 and arbitrary n.

References used

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HANSBERG, A; VOLKMANN, L. Upper bounds on the k-domination number and the k-Roman domination number. Discrete Appl. Math. 157 (2009), 1634-1639
BLIDIAA,M; CHELLALIA,M; VOLKMANNB,L. Some bounds on the pdomination number in trees. Discrete Mathematics, 306 (2006), 2031 – 2037

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