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 num- ber 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 ful- lerene graph C90 with original implication on IPR C90 isomers topological stability.

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