Journal of Mahani Mathematical Research (Aug 2024)

Neighborhood version of third Zagreb index of trees

  • Nasrin Dehgardi

DOI
https://doi.org/10.22103/jmmr.2024.22721.1559
Journal volume & issue
Vol. 13, no. 2
pp. 547 – 562

Abstract

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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.

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