Laplacian coefficients and Zagreb indices of trees

Abstract

Let G be a simple and undirected graph with Laplacian polynomial $\psi (G,\lambda )={\sum }_{k=0}^n{(-1)}^{n-k}{c}_k(G){\lambda }^k$. In earlier works, some formulas for computing $c_2(G)$, $c_{n-2}(G)$ and $c_{n-3}(G)$ in terms of the number of vertices, the Wiener, the first Zagreb and the forgotten indices are given. In this paper, we continue this work by computing $c_{n-4}(T)$, where T is a tree. A lower and an upper bound for $c_{n-4}(T)$ are obtained.

Keywords:

• Laplacian coefficient
• Zagreb index
• tree

AMS Subject Classifications:

• 05C31
• 05C05

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of the first author is partially supported by the University of Kashan [grant number 364988/169].