THE COMPLEMENT METRIC DIMENSION OF GRAPHS AND ITS OPERATIONS

Let G be a connected graph with vertex set V(G) and edge set E(G). The distance between vertices u and v in G is denoted by d(u, v), which serves as the shortest path length from u to v. Let be an ordered set, and v is a vertex in G. The representation of v with respect to W is an ordered set , | . The set W is called a resolving set for G if each vertex in G has a different representation with respect to W. A resolving set containing minimum cardinality is called a basis for G. The number of vertices in a basis of G is called metric dimension of G, which is denoted by . The is a complement resolving set of G if there are two vertices , such that | | . A complement basis of G is the complement resolving set containing maximum cardinality. The number of vertices in a complement basis of G is called complement metric dimension of G, which is denoted by ̅̅̅̅̅ . In this paper, we examined complement metric dimension of particular graphs and their characteristics. Furthermore, we determined complement metric dimension of corona and comb products graphs.