Results on Relatively Prime Domination Number of Vertex Switching of Some Graphs

Abstract

If a set S ⊆ V has at least two members and every pair of vertices u and v is such that (d(u), d(v)) = 1, then it is said to be a relatively prime dominating set. The relatively prime domination number, represented by γrpd(G), is the lowest cardinality of a relatively prime dominating set. The switching of a finite undirected graph by a subset is defined as the graph Gσ(V, E′), which is obtained from G by removing all edges between σ and its complement V − σ and adding as edges all non-edges between σ and V − σ. In this paper, we com- pute the relatively prime domination number of vertex switching of cycle type graphs like David Star Graph, Helm Graph, Friendship Graph and Book Graph.

Keywords

• dominating set, relatively prime dominating set, relatively prime domination number, vertex switching