On topological characterizations and entropies for algebraic structure graphs over Dihedral groups

An algebraic graph is defined in terms of graph theory as a graph with related algebraic structures or characteristics. If the vertex set of a graph [Formula: see text] is a group, a ring, or a field, then [Formula: see text] is called an algebraic structure graph. A graph [Formula: see text] is a commutative graph over a group if two distinct elements are adjacent if they commute with each other. In this work, a class of Dihedral groups is taken, and then a commutative graph is established. The edge partition mappings are computed based on the degree of each vertex of a commutative graph over a Dihedral group. Using these mappings, the [Formula: see text]-polynomials are computed for commutative graphs over Dihedral groups. The various topological indices and entropies are evaluated on the proposed family of commutative graphs over Dihedral groups.