Open AccessBounds on the first leap Zagreb index of trees
Author(s) -
Nasrin Dehgardi,
H. Aram
Publication year - 2021
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.13.2.377-385
Subject(s) - mathematics , combinatorics , vertex (graph theory) , graph , index (typography) , explained sum of squares , statistics , computer science , world wide web
The first leap Zagreb index $LM1(G)$ of a graph $G$ is the sum of the squares of its second vertex degrees, that is, $LM_1(G)=\sum_{v\in V(G)}d_2(v/G)^2$, 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.