Some new bounds on the general sum--connectivity index

Ali, Akbar; Javaid, Mubeen; Matejić, Marjan; Milovanović, Igor; Milovanović, Emina

doi:10.22049/cco.2019.26618.1125

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	Some new bounds on the general sum--connectivity index
Communications in Combinatorics and Optimization
مقاله 2، دوره 5، شماره 2، اسفند 2020، صفحه 97-109 اصل مقاله (390.27 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2019.26618.1125
نویسندگان
Akbar Ali¹؛ Mubeen Javaid¹؛ Marjan Matejić²؛ Igor Milovanović^* ³؛ Emina Milovanović²
¹Knowledge Unit of Science University of Management and Technology, Sialkot 51310, Pakistan
²Faculty of Electronic Engineering, 18000 Nis, Serbia
³Faculty of Electronic Engineering, Nis, Serbia
چکیده
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.
کلیدواژه‌ها
Topological indices؛ vertex degree؛ sum-connectivity index

مراجع
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Some new bounds on the general sum--connectivity index