@article {
author = {Gutman, Ivan and Shao, Zehui and Li, Zepeng and Wang, ShaohuiShaohui and We, Pu},
title = {Leap Zagreb indices of trees and unicyclic graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {3},
number = {2},
pages = {179-194},
year = {2018},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2018.26285.1092},
abstract = {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.},
keywords = {Leap Zagreb index,Zagreb index,degree (of vertex)},
url = {http://comb-opt.azaruniv.ac.ir/article_13782.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13782_6ae3457e7f09b8f6c913dd0fa53fa742.pdf}
}