# Leap Zagreb indices of trees and unicyclic graphs

Document Type : Original paper

Authors

1 University of Kragujevac

2 Guangzhou University

3 Lanzhou University

4 Department of Mathematics and Computer Science, Adelphi University, Garden City, NY, USA.

5 Guangzhou University,

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.

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