Article ID: MTJPAM-D-24-00057

Title: Some properties of the novel topological graph index atom-bond sum-connectivity index

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-24-00057; Volume 6 / Issue 3 / Year 2024, Pages 418-427

Document Type: Research Paper

Author(s): ‪Gowtham Kalkere Jayanna ^a , Narahari Narasimha Swamy ^b , Badekara Sooryanarayana ^c , Ismail Naci Cangul ^d

^aDepartment of Mathematics, University College of Science, Tumkur University, Tumakuru 572103, Karnataka, India

^bDepartment of Mathematics, University College of Science, Tumkur University, Tumakuru 572103, Karnataka, India

^cDepartment of Mathematics and Computational Studies, Dr. Ambedkar, Institute of Technology, Bengaluru 560056, Karnataka, India

^dDepartment of Mathematics, Bursa Uludag University, Gorukle 16059, Bursa, Turkey

Received: 20 April 2024, Accepted: 7 December 2024, Published: 13 April 2025

Corresponding Author: Ismail Naci Cangul (Email address: cangul@uludag.edu.tr)

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Abstract

The sum-connectivity variant of atom-bond connectivity index is recently introduced, and is defined as the sum of the terms of the form over all adjacent vertices u, v in a graph G, and named as the atom-bond sum connectivity index denoted by ABS(G). The sum of the absolute values of all the eigenvalues of the adjacency matrix of a graph G is known as the graph energy E(G). In this paper, we observe some mathematical properties of ABS(G) and establish bounds for this index in terms of other indices. We also compare ABS(T) with E(T) taking all trees T of order n = 8, 9, …, 14 and observe a very strong correlation between the two invariants for all studied groups of trees.

Keywords: Atom-bond sum-connectivity index, ABS, topological index, graph energy

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