On Secure Resolving Number of Networks

Abstract

Consider a graph G(V,E) that is simple, connected, and finite.The resolving set for G is defined as the subset of V(G) for which each vertex of G has a distinct representation and the minimal cardinality of such a subset is said to be the metric dimension of G.If for any m ∈V \T, there exists n ∈ T such that T −{n}∪{m} is a resolving set, then the resolving set T is called a secure resolving set. The secure metric dimension of a graph G is defined as the cardinality of the minimum secure resolving set. Establishing the secure metric dimension of a specific graph presents an NP complete challenge.The SMD of various graph networks is already defined and determined.In this thesis we have examined the exact value of secure resolving number of Web Graph W∗ n .