Determining the irregular chromatic number of graphs using a rank-based genetic algorithm
Zahra Hamed-Labbafian, Mostafa Tavakoli, Narjes Sabeghi, Ottorino Ori · Fullerenes Nanotubes and Carbon Nanostructures · 2025
Fullerene graph is a planar connected cubic graph whose faces are pentagons and hexagons. In this article, a rank-based genetic algorithm (RBGA) is presented to compute the irregular chromatic number of an undirected graph. In irregular coloring, each vertex must not only have a different color from its neighbors but also possess a unique color code. This code is a combination of the vertex color with the set of its neighbors’ colors. The aim is to find the minimum number of colors required to achieve this kind of coloring. The presented algorithm using rank-based selection, combination (crossover) and mutation operators to explore the search space effectively, aiming for convergence toward the near optimal solutions. The proposed algorithm is implemented on the isomers of the fullerene graph C90 with original implication on IPR C90 isomers topological stability.