Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21283220181201Leap Zagreb indices of trees and unicyclic graphs1791941378210.22049/cco.2018.26285.1092ENIvanGutmanUniversity of Kragujevac0000-0001-9681-1550ZehuiShaoGuangzhou UniversityZepengLiLanzhou UniversityShaohuiShaohuiWangDepartment of Mathematics and Computer Science, Adelphi University,
Garden City, NY, USA.PuWeGuangzhou University,Journal Article20180601By $d(v|G)$ 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.http://comb-opt.azaruniv.ac.ir/article_13782_6ae3457e7f09b8f6c913dd0fa53fa742.pdf