Open Journal of Discrete Applied Mathematics
Vol. 2 (2019), Issue 2, pp. 23 – 30
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2019.0013
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2019.0013
The smallest sum-connectivity index on trees with \(n\) vertices and \(k\) pendant vertices
Yuedan Yao\(^1\)
Department of Mathematics, South China Agricultural University, Guangzhou, 510642, P.R. China.
\(^{1}\)Corresponding Author: yaoyuedan12@163.com
Department of Mathematics, South China Agricultural University, Guangzhou, 510642, P.R. China.
\(^{1}\)Corresponding Author: yaoyuedan12@163.com
Copyright © 2019 Yuedan Yao. 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: April 15, 2019 – Accepted: May 21, 2019 – Published: June 25, 2019
Abstract
For a given connected graph \(G\) and a real number \(\alpha\), denote by \(d(u)\) the degree of vertex \(u\) of \(G\), and denote by \(\chi_{\alpha}(G)=\sum_{uv\in E(G)} \big(d(u)+d(v)\big)^{\alpha}\) the general sum-connectivity index of \(G\). In the present note, we determine the smallest general sum-connectivity index of trees (resp., chemical trees) together with corresponding extremal trees among all trees (resp., chemical trees) with \(n\) vertices and \(k\) pendant vertices for \(0<\alpha<1.\)
Keywords:
General sum-connectivity index, chemical trees, extremal trees.