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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University of Kashan
2025-06-01
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| Series: | Mathematics Interdisciplinary Research |
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| Online Access: | https://mir.kashanu.ac.ir/article_114890_4086ca2b1bbd37b77e9cca3d4e7d2f73.pdf |
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| author | Ali Ghalavand Alireza Ashrafi |
| author_facet | Ali Ghalavand Alireza Ashrafi |
| author_sort | Ali Ghalavand |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e279b690145a4ba5852c92e5b2a04ea2 |
| institution | Kabale University |
| issn | 2476-4965 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | University of Kashan |
| record_format | Article |
| series | Mathematics Interdisciplinary Research |
| spelling | doaj-art-e279b690145a4ba5852c92e5b2a04ea22025-08-20T03:32:07ZengUniversity of KashanMathematics Interdisciplinary Research2476-49652025-06-0110213314310.22052/mir.2024.255007.1467114890Laplacian Coefficients of a Forest in Terms of the Number of Closed Walks in the Forest and its Line GraphAli Ghalavand0Alireza Ashrafi1Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. IranDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. IranIn 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.https://mir.kashanu.ac.ir/article_114890_4086ca2b1bbd37b77e9cca3d4e7d2f73.pdfforestlaplacian coefficientclosed walk |
| spellingShingle | Ali Ghalavand Alireza Ashrafi Laplacian Coefficients of a Forest in Terms of the Number of Closed Walks in the Forest and its Line Graph Mathematics Interdisciplinary Research forest laplacian coefficient closed walk |
| title | Laplacian Coefficients of a Forest in Terms of the Number of Closed Walks in the Forest and its Line Graph |
| title_full | Laplacian Coefficients of a Forest in Terms of the Number of Closed Walks in the Forest and its Line Graph |
| title_fullStr | Laplacian Coefficients of a Forest in Terms of the Number of Closed Walks in the Forest and its Line Graph |
| title_full_unstemmed | Laplacian Coefficients of a Forest in Terms of the Number of Closed Walks in the Forest and its Line Graph |
| title_short | Laplacian Coefficients of a Forest in Terms of the Number of Closed Walks in the Forest and its Line Graph |
| title_sort | laplacian coefficients of a forest in terms of the number of closed walks in the forest and its line graph |
| topic | forest laplacian coefficient closed walk |
| url | https://mir.kashanu.ac.ir/article_114890_4086ca2b1bbd37b77e9cca3d4e7d2f73.pdf |
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