Trees with Maximum Vertex-Degree-Based Topological Indices

Abstract

Let G be a graph with vertex set V (G) = {v 1 , v 2 , . . ., v n } and edge set E(G), and d(v i ) be the degree of the vertex v i .The definition of a vertex-degree-based topological index of G is as followswhere f (x, y) > 0 is a symmetric real function with x > 0 and y > 0.In this paper, we find the extremal trees with the maximum vertex-degree-based topological index T f among all trees of order n when f (x, y) is increasing and concave up in respect to variable x (to variable y too, of course).

Topics & Concepts