On Adjacency Metric Dimension of Some Families of Graph. (25th June 2022) - Koam, Ali N. A.; Ahmad, Ali; Azeem, Muhammad; Khalil, Adnan; Nadeem, Muhammad Faisal
Abstract : Metric dimension of a graph is a well-studied concept. Recently, adjacency metric dimension of graph has been introduced. A set Q a ⊂ V G is considered to be an adjacency metric generator for G if u 1, u 2 ∈ V \ Q a (supposing each pair); there must exist a vertex q ∈ Q a along with the condition that q is indeed adjacent to one of u 1, u 2 . The minimum number of elements in adjacency metric generator is the adjacency metric dimension of G, denoted by di m a G . In this work, we compute exact values of the adjacency metric dimension of circulant graph C n 1, 2, Möbius ladder, hexagonal Möbius ladder, and the ladder graph.