Strong Edge Coloring in Tree-Like Networks

A strong edge coloring of a graph is a proper edge coloring such that no two edges within a distance of two share the same color. The strong chromatic index of the graph G is denoted by χ′ (G). Strong edge coloring is a variation of coloring problems and it has practical uses in various fields such as wireless communication, resource allocation, VLSI circuit design, and task scheduling. It is an extension of the traditional edge coloring that is used in communication networks, but it is more complex as it requires that no two edges within a distance of two share the same color, an idea that is implemented in different ways to allow for much more efficient use of spectrum. In our work, we design a heuristic algorithm based on edge degrees and recursive connectivity levels that gives priority to edge coloring, as a result of which we manage to minimize the color usage that ensures conflict-free color assignments with the smallest number of colors. This work is aimed at presenting an interdisciplinary prospect that blends formal mathematical studies on combinatorics with the practical use of fractal graph colorings, the theory of partitioning and network models with structure.