Vertex-degree-based topological indices over starlike trees

Given a graph GG with nn vertices, a vertex-degree-based topological index is defined from a set of real numbers {φij}{φij} as TI(G)=∑mij(G)φijTI(G)=∑mij(G)φij, where mij(G)mij(G) is the number of edges between vertices of degree ii and degree jj, and the sum runs over all 1≤i≤j≤n−11≤i≤j≤n−1. We find conditions on the numbers {φij}{φij} which are easy to verify, under which the extremal values of TITI 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 ΩnΩn.