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A note on the first Zagreb index and coindex of graphs | ||
Communications in Combinatorics and Optimization | ||
مقاله 4، دوره 6، شماره 1، شهریور 2021، صفحه 41-51 اصل مقاله (375.42 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2020.26809.1144 | ||
نویسندگان | ||
Igor Milovanović* 1؛ Marjan Matejić2؛ Emina Milovanović2؛ Rana Khoeilar3 | ||
1Faculty of Electronic Engineering, Nis, Serbia | ||
2Faculty of Electronic Engineering | ||
3Azarbaijan Shahid Madani University | ||
چکیده | ||
Let $G=(V,E)$, $V=\{v_1,v_2,\ldots,v_n\}$, be a simple graph with $n$ vertices, $m$ edges and a sequence of vertex degrees $\Delta=d_1\ge d_2\ge \cdots \ge d_n=\delta$, $d_i=d(v_i)$. If vertices $v_i$ and $v_j$ are adjacent in $G$, it is denoted as $i\sim j$, otherwise, we write $i\nsim j$. The first Zagreb index is vertex-degree-based graph invariant defined as $M_1(G)=\sum_{i=1}^nd_i^2$, whereas the first Zagreb coindex is defined as $\overline{M}_1(G)=\sum_{i\nsim j} d_i+d_j)$. A couple of new upper and lower bounds for $M_1(G)$, as well as a new upper bound for $\overline{M}_1(G)$, are obtained. | ||
کلیدواژهها | ||
Topological indices؛ first Zagreb index؛ first Zagreb coindex | ||
مراجع | ||
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