On Distance-Two Domination of Composition of Graphs

Abstract

For a graph G V,E, let 1 N (v) and 2 N (v) denote the set of vertices that are at distance one and two from v respectively. A subset DV Gis said to be a 3,2,1 D -dominating set of G if every vertex vV satisfies  3 D w v  where  D w v 3 vD  2  1 N v D   2 N v D . The minimum cardinality of a 3,2,1 D -dominating set of G , denoted as   3,2,1  G , is called the 3,2,1 D -domination number of G . In this paper we obtained the 3,2,1 D -domination number of the composition of two paths and a path with a cycle.