Vertex-Degree Based Topological Indices of Graphene
Juan Rada
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−1mi,j(G)φ(i,j), where mi,j=mi,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.
Topics & Concepts
Vertex (graph theory)GrapheneDegree (music)Topological indexCombinatoricsTopology (electrical circuits)Molecular graphGraphMathematicsDiscrete mathematicsPhysicsQuantum mechanicsAcousticsGraph theory and applicationsGraphene research and applicationsGraph Labeling and Dimension Problems