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Leap Zagreb indices of trees and unicyclic graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 6، دوره 3، شماره 2، پاییز و زمستان 2018، صفحه 179-194 اصل مقاله (434.37 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2018.26285.1092 | ||
| نویسندگان | ||
Ivan Gutman  1؛ Zehui Shao2؛ Zepeng Li3؛ ShaohuiShaohui Wang4؛ Pu We5
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| 1University of Kragujevac | ||
| 2Guangzhou University | ||
| 3Lanzhou University | ||
| 4Department of Mathematics and Computer Science, Adelphi University, Garden City, NY, USA. | ||
| 5Guangzhou University, | ||
| چکیده | ||
| By $d(v|G)$ and $d_2(v|G)$ are denoted the number of first and second neighbors of the vertex $v$ of the graph $G$. The first, second, and third leap Zagreb indices of $G$ are defined as $LM_1(G) = \sum_{v \in V(G)} d_2(v|G)^2$, $LM_2(G) = \sum_{uv \in E(G)} d_2(u|G)\,d_2(v|G)$, and $LM_3(G) = \sum_{v \in V(G)} d(v|G)\,d_2(v|G)$, respectively. In this paper, we generalize the results of Naji et al. [Commun. Combin. Optim. {\bf 2} (2017), 99--117], pertaining to trees and unicyclic graphs. In addition, we determine upper and lower bounds on these leap Zagreb indices and characterize the extremal graphs. | ||
| کلیدواژه‌ها | ||
| Leap Zagreb index؛ Zagreb index؛ degree (of vertex) | ||
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آمار تعداد مشاهده مقاله: 755 تعداد دریافت فایل اصل مقاله: 657 |
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