On Adjacency Metric Dimension of Some Families of Graph

Abstract

Metric dimension of a graph is a well-studied concept. Recently, adjacency metric dimension of graph has been introduced. A set Qa⊂VG is considered to be an adjacency metric generator for G if u1,u2∈V\Qa (supposing each pair); there must exist a vertex q∈Qa along with the condition that q is indeed adjacent to one of u1,u2. The minimum number of elements in adjacency metric generator is the adjacency metric dimension of G, denoted by dimaG. In this work, we compute exact values of the adjacency metric dimension of circulant graph Cn1,2, Möbius ladder, hexagonal Möbius ladder, and the ladder graph.