Bounds on the first leap Zagreb index of trees

  • N. Dehgardi Sirjan University of Technology, Sirjan, Iran
  • H. Aram Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran
Keywords: tree, first leap Zagreb index, Zagreb index
Published online: 2021-08-19


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.

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How to Cite
Dehgardi N., Aram H. Bounds on the First Leap Zagreb Index of Trees. Carpathian Math. Publ. 2021, 13 (2), 377-385.