Note on PI and Szeged indices

TL;DR

This paper investigates distance-based graph invariants used in chemistry, providing improved inequalities and characterizations of extremal graphs for PI, Szeged, and related indices.

Contribution

It introduces new sharp inequalities and complete characterizations for extremal graphs concerning PI, Szeged, and related indices, enhancing theoretical understanding.

Findings

Derived improved inequalities for topological indices.

Provided complete extremal graph characterizations.

Linked indices to graph parameters like vertices, edges, and triangles.

Abstract

In theoretical chemistry molecular structure descriptors are used for modeling physico-chemical, pharmacological, toxicologic, biological and other properties of chemical compounds. In this paper we study distance-based graph invariants and present some improved and corrected sharp inequalities for PI, vertex PI, Szeged and edge Szeged topological indices, involving the number of vertices and edges, the diameter, the number of triangles and the Zagreb indices. In addition, we give a complete characterization of the extremal graphs.