On the distance paired domination of generalized Petersen graphs P(n,1) and P(n,2)

Abstract

Let G=(V,E) be a graph without an isolated vertex. A set D?V(G) is a k -distance paired dominating set of G if D is a k-distance dominating set of G and the induced subgraph ?D? has a perfect matching. The minimum cardinality of a k-distance paired dominating set for graph G is the k -distance paired domination number, denoted by ? p k (G). In this paper, we determine the exact k-distance paired domination number of generalized Petersen graphs P(n,1) and P(n,2) for all k?1.