Neighborhood version of third Zagreb index of trees

Author(s):

Nasrin Dehgardi *

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
For a graph $G$, the third neighborhood degree index of $G$ is defined as: $$ND_3(G)=\sum_{ab\in E(G)}\delta_G(a)\delta_G(b)\Big(\delta_G(a)+\delta_G(b)\Big),$$ where $\delta_G(a)$ represents the sum of degrees of all neighboring vertices of vertex $a$. In this short paper, we establish a new lower bound on the third neighborhood degree index of trees and characterize the extremal trees achieving this bound.
Keywords:

Third Neighborhood Degree Index‎ , ‎Trees‎ , ‎Lower Bound‎

Language:
English
Published:
Journal of Mahani Mathematical Research, Volume:13 Issue: 2, Summer and Autumn 2024
Pages:
547 to 562
https://www.magiran.com/p2753624