Comparison of Topological Indices Based on Iterated ‘Sum’ versus ‘Product’ Operations

BALABAN, A. T.; KHADIKAR, P. V.; AZIZ, S.

doi:10.22052/ijmc.2010.5134

Comparison of Topological Indices Based on Iterated ‘Sum’ versus ‘Product’ Operations

Document Type : Research Paper

Authors

A. T. BALABAN ¹

P. V. KHADIKAR ²

S. AZIZ ³

¹ Texas A&M University at Galveston, USA

² Khatipura, Indore India

³ Institute of Engineering and Technology, India

10.22052/ijmc.2010.5134

Abstract

The Padmakar-Ivan (PI) index is a first-generation topological index (TI) based on sums over all edges between numbers of edges closer to one endpoint and numbers of edges closer to the other endpoint. Edges at equal distances from the two endpoints are ignored. An analogous definition is valid for the Wiener index W, with the difference that sums are replaced by products. A few other TIs are discussed, and comparisons are made between them. The best correlation is observed between indices G and PI; satisfactory correlations exist between W/n3 and PI/n2, where n denotes the number of vertices in the hydrogen-depleted graph.

Keywords

Topological indices

PI index

Balaban index J

Wiener index W

F and G indices