On the local metric dimension of corona product graphs

TL;DR

This paper investigates the local metric dimension of corona product graphs, providing exact values and insights into how these dimensions are determined based on the properties of the component graphs.

Contribution

It offers the first comprehensive analysis and exact formulas for the local metric dimension of corona product graphs, expanding understanding in graph metric theory.

Findings

Derived exact formulas for local metric dimension of corona product graphs

Identified how component graph properties influence the local metric dimension

Enhanced theoretical understanding of vertex distinguishing in complex graph structures

Abstract

A vertex $v\in V(G)$ is said to distinguish two vertices $x,y\in V(G)$ of a nontrivial connected graph $G$ if the distance from $v$ to $x$ is different from the distance from $v$ to $y$. A set $S\subset V(G)$ is a local metric generator for $G$ if every two adjacent vertices of $G$ are distinguished by some vertex in $S$. A local metric generator with the minimum cardinality is called a local metric basis for $G$ and its cardinality, the local metric dimension of G. In this paper we study the problem of finding exact values for the local metric dimension of corona product of graphs.