On the Constant Edge Resolvability of Some Unicyclic and Multicyclic Graphs

Abstract

Assume that G = V G , E G is a connected graph. For a set of vertices W E ⊆ V G , two edges g 1 , g 2 ∈ E G are distinguished by a vertex x 1 ∈ W E , if d x 1 , g 1 ≠ d x 1 , g 2 . W E is termed edge metric generator for G if any vertex of W E distinguishes every two arbitrarily distinct edges of graph G . Furthermore, the edge metric dimension of G , indicated by edim G , is the cardinality of the smallest W E for G . The edge metric dimensions of the dragon, kayak paddle, cycle with chord, generalized prism, and necklace graphs are calculated in this article.