New Bounds for Topological Indices on Trees through Generalized Methods

Abstract

Topological indices are useful for predicting the physicochemical behavior of chemical compounds. A main problem in this topic is finding good bounds for the indices, usually when some parameters of the graph are known. The aim of this paper is to use a unified approach in order to obtain several new inequalities for a wide family of topological indices restricted to trees and to characterize the corresponding extremal trees. The main results give upper and lower bounds for a large class of topological indices on trees, fixing or not the maximum degree. This class includes the first variable Zagreb, the Narumi–Katayama, the modified Narumi–Katayama and the Wiener index.

Keywords

• first variable zagreb index
• Narumi–Katayama index
• modified Narumi–Katayama index
• Wiener index
• topological indices
• Schur-convexity