Laplacian Coefficients of a Forest in Terms of the Number of Closed Walks in the Forest and its Line Graph
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Kashan
2025-06-01
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| Series: | Mathematics Interdisciplinary Research |
| Subjects: | |
| Online Access: | https://mir.kashanu.ac.ir/article_114890_4086ca2b1bbd37b77e9cca3d4e7d2f73.pdf |
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| Summary: | 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. |
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| ISSN: | 2476-4965 |