On the Constant Edge Resolvability of Some Unicyclic and Multicyclic Graphs

Abstract

Assume that G=VG,EG is a connected graph. For a set of vertices WE⊆VG, two edges g1,g2∈EG are distinguished by a vertex x1∈WE, if dx1,g1≠dx1,g2. WE is termed edge metric generator for G if any vertex of WE distinguishes every two arbitrarily distinct edges of graph G. Furthermore, the edge metric dimension of G, indicated by edimG, is the cardinality of the smallest WE for G. The edge metric dimensions of the dragon, kayak paddle, cycle with chord, generalized prism, and necklace graphs are calculated in this article.