Vertex-degree-based topological indices over trees with two branching vertices

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 T I (G) = Pmij (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. Let Ω (n, 2) denote the set of all trees with n vertices and 2 branching vertices. In this paper we give conditions on the number {φij} under which the extremal trees with respect to T I can be determined. As a consequence, we find extremal trees in Ω (n, 2) for several well-known vertex-degree- based topological indices.