Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21285220201201Some new bounds on the general sum--connectivity index971091398710.22049/cco.2019.26618.1125ENAkbarAliKnowledge Unit of Science
University of Management and Technology, Sialkot 51310, Pakistan0000-0001-8160-4196MubeenJavaidKnowledge Unit of Science
University of Management and Technology, Sialkot 51310, PakistanMarjanMatejiÄ‡Faculty of Electronic Engineering, 18000 Nis, SerbiaIgorMilovanoviÄ‡Faculty of Electronic Engineering, Nis, SerbiaEminaMilovanoviÄ‡Faculty of Electronic Engineering, 18000 Nis, SerbiaJournal Article20190718Let $G=(V,E)$ 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 $v_iin V$. With $isim j$ we denote adjacency of vertices $v_i$ and $v_j$. The general sum--connectivity index of graph is defined as $chi_{alpha}(G)=sum_{isim j}(d_i+d_j)^{alpha}$, 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.http://comb-opt.azaruniv.ac.ir/article_13987_cdec3088e115acb1295b55b1ba267a6e.pdf