Metric dimension, doubly resolving set and strong metric dimension for $(C_n\Box P_k)\Box P_m$

TL;DR

This paper investigates the minimum size of doubly resolving sets and related metric parameters for the graph product $(C_n\Box P_k)\Box P_m$, contributing to the understanding of metric dimensions in complex graph structures.

Contribution

It provides a computational study of the minimum resolving sets for the specific graph product $(C_n\Box P_k)\Box P_m$, which is a novel analysis in this context.

Findings

Determined the minimum size of doubly resolving sets for the given graph product.

Established bounds or exact values for the metric dimension parameters.

Enhanced understanding of resolving sets in complex graph products.

Abstract

A subset $Q = \{q_1, q_2, ..., q_l\}$ of vertices of a connected graph $G$ is a doubly resolving set of $G$ if for any various vertices $x, y \in V(G)$ we have $r(x|Q)-r(y|Q)\neq\lambda I$, where $\lambda$ is an integer, and $I$ indicates the unit $l$- vector $(1,..., 1)$. A doubly resolving set of vertices of graph $G$ with the minimum size, is denoted by $\psi(G)$. In this work, we will consider the computational study of some resolving sets with the minimum size for $(C_n\Box P_k)\Box P_m$.