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A vast amount of information about distance based graph invariants is contained in the Hosoya polynomial. Such an information is helpful to determine well-known distance based molecular descriptors. The Hosoya index or  Z -index of a graph  G  is the total number of its matching. The Hosoya index is a prominent example of topological indices, which are of great interest in combinatorial chemistry, and later on it applies to address several chemical properties in molecular structures. In this article, we investigate Hosoya properties (Hosoya polynomial, reciprocal Hosoya polynomial and Hosoya index) of the commuting graph associated with an algebraic structure developed by the symmetries of regular molecular gones (constructed by atoms with regular atomic-bonding).

Hosoya properties of the commuting graph associated with the group of symmetries