Open Journal of Discrete Applied Mathematics
Vol. 7 (2024), Issue 2, pp. 11 – 22
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2024.0099
On the eccentric atom-bond sum-connectivity index
Zaryab Hussain\(^{1,*}\), Muhammad Ahsan Binyamin\(^{2}\)
\(^{1}\) School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, Shaanxi 710129, China; zaryabhussain2139@gmail.com
\(^{2}\) Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan; ahsanbanyamin@gmail.com
Copyright © 2024 Zaryab Hussain, Muhammad Ahsan Binyamin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: June 9, 2024 – Accepted: June 29, 2024 – Published: June 30, 2024
Abstract
The eccentric atom-bond sum-connectivity \(\left(ABSC_{e}\right)\) index of a graph \(G\) is defined as \(ABSC_{e}(G)=\sum\limits_{uv\in E(G)}\sqrt{\frac{e_{u}+e_{v}-2}{e_{u}+e_{v}}}\), where \(e_{u}\) and \(e_{v}\) represent the eccentricities of \(u\) and \(v\) respectively. This work presents precise upper and lower bounds for the \(ABSC_{e}\) index of graphs based on their order, size, diameter, and radius. Moreover, we find the maximum and minimum \(ABSC_{e}\) index of trees based on the specified matching number and the number of pendent vertices.
Keywords:
eccentric atom-bond sum-connectivity index; tree; matching number; pendent vertex