On the Edge Metric Dimension of Different Families of Möbius Networks

Abstract

For an ordered subset Q e of vertices in a simple connected graph G , a vertex x ∈ V distinguishes two edges e 1 , e 2 ∈ E , if d x , e 1 ≠ d x , e 2 . A subset Q e having minimum vertices is called an edge metric generator for G , if every two distinct edges of G are distinguished by some vertex of Q e . The minimum cardinality of an edge metric generator for G is called the edge metric dimension, and it is denoted by dim e G . In this paper, we study the edge resolvability parameter for different families of Möbius ladder networks and we find the exact edge metric dimension of triangular, square, and hexagonal Möbius ladder networks.

On the Edge Metric Dimension of Certain Polyphenyl Chains

“…Wei et al studied the edim of some complex convex polytopes in [21]. Deng et al computed the edim of triangular, square, and hexagonal Mobius ladder networks in [22]. Ahmad et al calculated the edim of the benzenoid tripod structure in [23].…”

The Vertex-Edge Resolvability of Some Wheel-Related Graphs

“…Metric dimension has various significant applications in computer science, mathematics, social sciences, chemical sciences, etc. [4][5][6][7][8][9][10][11][12][13][14].…”

Computation of Edge Resolvability of Benzenoid Tripod Structure

“…Assume that C is an associated graph of chemical structure/network, whose vertex/node set are denoted by symbol N(C) or simply N, while B(C) or B is the edge/bond set, and the shortest distance between two bonds b 1 , b 2 ∈ N(C) is denoted by S b 1 ,b 2 and calculated by counting the number of bonds while moving through the b 1 − b 2 path. Definition 2 (see [32]). Assuming a subset of selected nodes λ e , if the position p(e|λ e ) of each edge e is unique of a graph, then λ e is called as edge metric resolving set and dim e (C) is the minimum count of members of λ e , called as edge metric dimension.…”