Edge Metric Dimension of Some Classes of Toeplitz Networks
Dalal Awadh Alrowaili, Zohaib Zahid, Muhammad Ahsan, Sohail Zafar, Imran Siddique · Journal of Mathematics · 2021
Toeplitz networks are used as interconnection networks due to their smaller diameter, symmetry, simpler routing, high connectivity, and reliability. The edge metric dimension of a network is recently introduced, and its applications can be seen in several areas including robot navigation, intelligent systems, network designing, and image processing. For a vertex s and an edge g = s 1 s 2 of a connected graph G , the minimum number from distances of s with s 1 and s 2 is called the distance between s and g . If for every two distinct edges s 1 , s 2 ∈ E G , there always exists w 1 ɛ W E ⊆ V G , such that d s 1 , w 1 ≠ d s 2 , w 1 ; then, W E is named as an edge metric generator. The minimum number of vertices in W E is known as the edge metric dimension of G . In this study, we consider four families of Toeplitz networks T n 1,2