On minimal edge version of doubly resolving sets of a graph

TL;DR

This paper introduces the edge version of doubly resolving sets in graphs, focusing on their minimal size in specific graph families, and provides exact computations for sunlet and prism graphs.

Contribution

It defines the edge doubly resolving set concept and calculates its minimum size for sunlet and prism graphs, advancing understanding of graph resolving sets.

Findings

Computed minimum edge doubly resolving set size for sunlet graphs.

Determined minimum edge doubly resolving set size for prism graphs.

Established foundational results for edge resolving sets in specific graph families.

Abstract

In this paper, we introduce the edge version of doubly resolving set of a graph which is based on the edge distances of the graph. As a main result, we computed the minimum cardinality $\psi_E$ of edge version of doubly resolving sets of family of $n$-sunlet graph $S_n$ and prism graph $Y_n$.