The distance spectrum of the line graph of the crown graph
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915568880189440 |
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| author | Mirafzal, S. Morteza |
| author_facet | Mirafzal, S. Morteza |
| contents | The distance eigenvalues of a connected graph $G$ are the eigenvalues of its distance matrix $D(G)$. A graph is called distance integral if all of its distance eigenvalues are integers. Let $n \geq 3$ be an integer. The crown graph $Cr(n)$ is a graph obtained from the complete bipartite graph $K_{n,n}$ by removing a perfect matching. Let $L(Cr(n))$ denote the line graph of the crown graph $Cr(n)$. Using the equitable partition method, the set of distinct distance eigenvalues of the graph $L(Cr(n))$ has been determined which shows that this graph is distance integral [S.Morteza Mirafzal, The line graph of the crown graph is distance integral, Linear and Multilinear Algebra 71, no. 4 (2023): 662-672]. The distance spectrum of the graph $L(Cr(n))$ has not been found yet. In this paper, having the set of distance eigenvalues of $L(Cr(n))$ in the hand, we determine the distance spectrum of this graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07202 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The distance spectrum of the line graph of the crown graph Mirafzal, S. Morteza Combinatorics The distance eigenvalues of a connected graph $G$ are the eigenvalues of its distance matrix $D(G)$. A graph is called distance integral if all of its distance eigenvalues are integers. Let $n \geq 3$ be an integer. The crown graph $Cr(n)$ is a graph obtained from the complete bipartite graph $K_{n,n}$ by removing a perfect matching. Let $L(Cr(n))$ denote the line graph of the crown graph $Cr(n)$. Using the equitable partition method, the set of distinct distance eigenvalues of the graph $L(Cr(n))$ has been determined which shows that this graph is distance integral [S.Morteza Mirafzal, The line graph of the crown graph is distance integral, Linear and Multilinear Algebra 71, no. 4 (2023): 662-672]. The distance spectrum of the graph $L(Cr(n))$ has not been found yet. In this paper, having the set of distance eigenvalues of $L(Cr(n))$ in the hand, we determine the distance spectrum of this graph. |
| title | The distance spectrum of the line graph of the crown graph |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.07202 |