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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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