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.