Optimal radio labeling for the Cartesian product of square mesh networks and stars

TL;DR

This paper investigates the optimal radio labeling problem for the Cartesian product of square mesh networks and star networks, providing bounds and exact values to improve channel assignment strategies in large communication networks.

Contribution

It derives the lower bounds and exact optimal radio label values for the Cartesian product of square mesh and star networks, a novel analysis for such network topologies.

Findings

Established lower bounds for the radio labeling problem.

Calculated exact optimal radio label values for specific network topologies.

Enhanced understanding of channel assignment in complex network structures.

Abstract

As the most critical component in the communication process, channels have a great impact on the communication quality of network. With the continuous expansion of network scale, the limited channel resources lead to the limitation of communication network scale. Therefore, achieving reasonable channel assignment and utilization becomes an extremely challenging problem. In order to solve this issue effectively, the channel assignment problem in communication networks can be transformed into a graph labeling problem, utilizing graphs to simulate the communication networks. In this paper, the topologies of mesh networks and stars are studied by constructing Cartesian product, and the lower bound and exact value of the optimal radio label of the Cartesian product of square mesh network and star $G=P(m,m)\Box K_{1,n}$ are obtained, where $m\geq 2$.