%0 Journal Article
%T Some new bounds on the general sum--connectivity index
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Ali, Akbar
%A Javaid, Mubeen
%A MatejiÄ‡, Marjan
%A MilovanoviÄ‡, Igor
%A MilovanoviÄ‡, Emina
%D 2020
%\ 12/01/2020
%V 5
%N 2
%P 97-109
%! Some new bounds on the general sum--connectivity index
%K Topological indices
%K vertex degree
%K sum-connectivity index
%R 10.22049/cco.2019.26618.1125
%X 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 $v_iin V$. 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.
%U http://comb-opt.azaruniv.ac.ir/article_13987_cdec3088e115acb1295b55b1ba267a6e.pdf