Edge resolvability of generalized honeycomb rhombic torus

Abstract

Minimum resolving sets (edge or vertex) have become integral to computer science, molecular topology, and combinatorial chemistry. Resolving sets for a specific network provide crucial information required for uniquely identifying each item in the network. The metric(respectively edge metric) dimension of a graph is the smallest number of the nodes needed to determine all other nodes (resp. edges) based on shortest path distances uniquely. Metric and edge metric dimensions as graph invariants have numerous applications, including robot navigation, pharmaceutical chemistry, canonically labeling graphs, and embedding symbolic data in low-dimensional Euclidean spaces. A honeycomb torus network can be obtained by joining pairs of nodes of degree two of the honeycomb mesh. Honeycomb torus has recently gained recognition as an attractive alternative to existing torus interconnection networks in parallel and distributed applications. In this article, we will discuss the Honeycomb Rhombic torus graph on the basis of edge metric dimension.