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arXiv · 2104.08476

Laplacian Coefficients of a Forest in terms of the Number of Closed Walks in the Forest and its Line Graph

Ali Ghalavand·Ali Reza Ashrafi
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Abstract

Let $G$ be a finite simple graph with Laplacian polynomial $\psi(G,\lambda)=\sum_{k=0}^n(-1)^{n-k}c_k\lambda^k$. In an earlier paper, the coefficients $c_{n-4}$ and $c_{n-5}$ for tree with respect to some degree-based graph invariants were computed. The aim of this paper is to continue this work by giving an exact formula for the coefficients $c_{n-6}$. As a consequence of this work, the Laplacian coefficients $c_{n-k}$ of a forest $F$, $1\leq k \leq 6$, are computed in terms of the number of closed walks in $F$ and its line graph.

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Ali Ghalavand, Ali Reza Ashrafi. 2021-04-17. Laplacian Coefficients of a Forest in terms of the Number of Closed Walks in the Forest and its Line Graph. https://arxiv.org/abs/2104.08476

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