Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 5 2 2020 12 01 Some new bounds on the general sum--connectivity index 97 109 13987 10.22049/cco.2019.26618.1125 EN Akbar Ali Knowledge Unit of Science University of Management and Technology, Sialkot 51310, Pakistan Mubeen Javaid Knowledge Unit of Science University of Management and Technology, Sialkot 51310, Pakistan Marjan Matejić Faculty of Electronic Engineering, 18000 Nis, Serbia Igor Milovanović Faculty of Electronic Engineering, Nis, Serbia Emina Milovanović Faculty of Electronic Engineering, 18000 Nis, Serbia Journal Article 2019 07 18 Let $G=(V,E)$ be a simple connected graph with $n$ vertices, $m$ edges and sequence of vertex degrees $d_1 \ge d_2 \ge \cdots \ge d_n>0$, $d_i=d(v_i)$, where $v_i\in V$. With $i\sim j$ we denote adjacency of vertices $v_i$ and $v_j$. The general sum--connectivity index of graph is defined as $\chi_{\alpha}(G)=\sum_{i\sim j}(d_i+d_j)^{\alpha}$, where $\alpha$ is an arbitrary real number. In this paper we determine relations between $\chi_{\alpha+\beta}(G)$ and $\chi_{\alpha+\beta-1}(G)$, where $\alpha$ and $\beta$ are arbitrary real numbers, and obtain new bounds for $\chi_{\alpha}(G)$. Also, by the appropriate choice of parameters $\alpha$ and $\beta$, we obtain a number of old/new inequalities for different vertex--degree--based topological indices. https://comb-opt.azaruniv.ac.ir/article_13987_cdec3088e115acb1295b55b1ba267a6e.pdf