Leap Zagreb indices of trees and unicyclic graphs

Document Type : Original paper


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,


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. 2 (2017), 99-117], pertaining to
trees and unicyclic graphs. In addition, we determine upper and lower bounds
for these leap Zagreb indices and characterize the extremal graphs.


Main Subjects