Vertex-Degree Based Topological Indices of Graphene. (21st April 2022) - Rada, Juan
Abstract: A vertex-degree-based (VDB, for short) topological index φ is defined for a graph G with n vertices as φ ( G ) = ∑ 1 ≤ i ≤ j ≤ n − 1 m i, j ( G ) φ ( i, j ), where m i, j = m i, j ( G ) is the number of edges of G joining a vertex of degree i with a vertex of degree j, and { φ ( i, j ) } is a set of real numbers. In this paper, we present a general formula to calculate VDB topological indices of graphene systems. As a byproduct, we solve the following extremal value problem: given a VDB topological index φ, find the graphene with maximal value of φ and the graphene with minimal value of φ, among all graphene with h hexagons.