Comprehensive study determines chromatic number and explores indices in graph structure, indicating significant interrelations.
In this paper, we present a comprehensive study of the maximal graph M(Γ(ℤ n )), constructed over the ring of integers modulo n, ℤ n . We determine the chromatic number of M(Γ(ℤ n )) in terms of the vertex cardinality of its specific induced subgraphs. We examine the interplay between topological indices, specifically the Sombor index and Wiener index with the Laplacian matrix, revealing a deeper understanding of their connections.
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Bora et al. (2026) studied this question.
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