ON METRIC DIMENSION OF BOOLEAN GRAPH BG1(G)

Abstract

Let G be a simple graph with vertex set V and edge set E. BG,NINC,Kq (G), known as boolean graph of G-first kind,simply denoted by BG1(G) is defined as the graph with vertex set V E and two vertices are adjacent if and only if they correspond to adjacent vertices in G or to a vertex and an edge in G such that the edge is not incident with the vertex. In this paper we give a bound for metric dimension of BG1(G) and also find expression for metric dimension of boolean graphs of Complete graphs and Star graphs. Finally, an algorithm for finding the metric dimension of BG1(G) is established.