Optimizing Balanced Networks with Strong Equitable Edge Colouring

Abstract

Equitable edge colouring is a sophisticated network labelling technique with no more than one difference in the number of edges between any two colour groups. In this study, we applied the equitable edge-coloring technique to triangulated networks, utilizing the minimal number of edge colours, denoted by Δ. The structural characteristics of horse stride, branch flow, and tri-wing networks are presented in this research. The technique ensures optimized network performance, regardless of whether the triangular graphs involved are in even or odd quantities, reinforcing the robustness of this method across diverse network architectures.