Neighborhood version of third Zagreb index of trees

Document Type : Research Paper

Author

Department of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, I.R. Iran

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.

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References

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History

  • Receive Date: 26 December 2023
  • Revise Date: 14 May 2024
  • Accept Date: 12 July 2024

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