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On the first and second Zagreb indices of quasi unicyclic graphs | ||
| Transactions on Combinatorics | ||
| مقاله 14، دوره 8، شماره 3، آذر 2019، صفحه 31-40 اصل مقاله (439.84 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2019.115147.1615 | ||
| نویسندگان | ||
| Majid Aghel1؛ Ahmad Erfanian* 2؛ Ali Reza Ashrafi3 | ||
| 1Ferdowsi University of Mashhad, International Campus | ||
| 2Ferdowsi University | ||
| 3University of Kashan | ||
| چکیده | ||
| Let $G$ be a simple graph. The graph $G$ is called a quasi unicyclic graph if there exists a vertex $x \in V(G)$ such that $G-x$ is a connected graph with a unique cycle. Moreover, the first and the second Zagreb indices of $G$ denoted by $M_1(G)$ and $M_2(G)$, are the sum of $\deg^2(u)$ overall vertices $u$ in $G$ and the sum of $\deg(u)\deg(v)$ of all edges $uv$ of $G$, respectively. The first and the second Zagreb indices are defined relative to the degree of vertices. In this paper, sharp upper and lower bounds for the first and the second Zagreb indices of quasi unicyclic graphs are given. | ||
| کلیدواژه‌ها | ||
| First Zagreb index؛ Second Zagreb index؛ Quasi Unicyclic graphs | ||
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آمار تعداد مشاهده مقاله: 316 تعداد دریافت فایل اصل مقاله: 393 |
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