The distance 2-resolving domination number of graphs

Abstract

The distance 2-resolving dominating set is the combination of two concepts, the resolving set and the distance 2-dominating set. The distance 2-resolving dominating set is a set that is both a distance 2-dominating set and a resolving set. The distance 2-resolving domination number is the minimum cardinality of a distance 2-resolving dominating set, denoted by ?2 (G). In this study, we define the distance 2-resolving dominating sets, and we examine distance 2-resolving domination number of graphs. We give the exact value of the distance 2-resolving domination number of complete graph, star graph, friendship graph and path graph.