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On trees and the multiplicative sum Zagreb index | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 4، دوره 1، شماره 2، اسفند 2016، صفحه 137-148 اصل مقاله (727.17 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2016.13574 | ||
| نویسندگان | ||
| Mehdi Eliasi* 1؛ Ali Ghalavand2 | ||
| 1Dept. of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran, | ||
| 2Dept. of Mathematics, Khansar Faculty of Mathematics and Computer Science, Khansar, Iran | ||
| چکیده | ||
| For a graph $G$ with edge set $E(G)$, the multiplicative sum Zagreb index of $G$ is defined as $\Pi^*(G)=\Pi_{uv\in E(G)}[d_G(u)+d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$. In this paper, we first introduce some graph transformations that decrease this index. In application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum Zagreb indices among all trees of order $n\geq 13$. | ||
| کلیدواژهها | ||
| Multiplicative Sum Zagreb Index؛ Graph Transformation؛ Branching Point؛ trees | ||
| مراجع | ||
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