Bounds on the first leap Zagreb index of trees - Dehgardi, N.; Aram, H. (Carpathian Mathematical Publications, 2021)
The first leap Zagreb index LM1(G) of a graph G is the sum of the squares of its second vertex degrees, that is, LM_1(G)=_vV(G)d_2(v/G)^2, where d_2(v/G) is the number of second neighbors of v in G. In this paper, we obtain bounds for the first leap Zagreb index of trees and determine the extremal trees achieving these bounds.