Laplacian Coefficients of a Forest in Terms of the Number of Closed Walks in the Forest and its Line Graph
نویسندگان
1 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. Iran
2 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. Iran
doi
10.22052/mir.2024.255007.1467چکیده
In this paper, we deal with calculating the laplacian coefficients of a finite simple graph $G$ with the Laplacian polynomial $\psi(G,\lambda) = \sum_{k=0}^{n}(-1)^{n-k}c_k\lambda^k$. We also explore the relationship between the number of closed walks in a graph and a series of its line graphs with the Laplacian coefficients. Our objective is to find a way to determine the Laplacian coefficients using the number of closed walks in a graph and its line graph. Specifically, we have derived the Laplacian coefficients $c_{n-k}$ of a forest $F$ (where $1 \leq k \leq 6$) in terms of the number of closed walks in $F$ and its line graph.
