Vertex-degree-based topological indices over starlike trees

Abstract

ABSTRACT: Given a graph G with n vertices, a vertex-degree-based topological index is defined from a set of real numbers {φij} as TI(G)=∑mij(G)φij, where mij(G) is the number of edges between vertices of degree i and degree j, and the sum runs over all 1≤i≤j≤n−1. We find conditions on the numbers {φij} which are easy to verify, under which the extremal values of TI over the set of starlike trees can be calculated. As an application we find the extremal values of many well-known vertex-degree-based topological indices over Ωn.