Leap Zagreb indices of trees and unicyclic graphs

Gutman, Ivan; Shao, Zehui; Li, Zepeng; Wang, ShaohuiShaohui; We, Pu

doi:10.22049/cco.2018.26285.1092

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	Leap Zagreb indices of trees and unicyclic graphs
Communications in Combinatorics and Optimization
مقاله 6، دوره 3، شماره 2، اسفند 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
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)

مراجع
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Leap Zagreb indices of trees and unicyclic graphs