THE COMPLEMENT METRIC DIMENSION OF GRAPHS AND ITS OPERATIONS
Journal Title: International Journal of Civil Engineering and Technology - Year 2019, Vol 10, Issue 3
Abstract
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.
Authors and Affiliations
L. SUSILOWATI, SLAMIN AND A. ROSFIANA
Keywords
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