On the Laplacian spectrum of $k$-symmetric graphs
For some positive integer $k$, if the finite cyclic group $\mathbb{Z}_k$ can act freely on a graph $G$, then we say that $G$ is $k$-symmetric. In 1985, Faria showed that the multiplicity of Laplacian eigenvalue 1 is greater than or equal to the difference between the number of pendant vertices and t...
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| creator | Moon, Sunyo Yoo, Hyungkee |
| description | For some positive integer $k$, if the finite cyclic group $\mathbb{Z}_k$ can
act freely on a graph $G$, then we say that $G$ is $k$-symmetric. In 1985,
Faria showed that the multiplicity of Laplacian eigenvalue 1 is greater than or
equal to the difference between the number of pendant vertices and the number
of quasi-pendant vertices. But if a graph has a pendant vertex, then it is at
most 1-connected. In this paper, we investigate a class of 2-connected
$k$-symmetric graphs with a Laplacian eigenvalue 1. We also identify a class of
$k$-symmetric graphs in which all Laplacian eigenvalues are integers. |
| doi_str_mv | 10.48550/arxiv.2211.11164 |
| format | Article |
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act freely on a graph $G$, then we say that $G$ is $k$-symmetric. In 1985,
Faria showed that the multiplicity of Laplacian eigenvalue 1 is greater than or
equal to the difference between the number of pendant vertices and the number
of quasi-pendant vertices. But if a graph has a pendant vertex, then it is at
most 1-connected. In this paper, we investigate a class of 2-connected
$k$-symmetric graphs with a Laplacian eigenvalue 1. We also identify a class of
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act freely on a graph $G$, then we say that $G$ is $k$-symmetric. In 1985,
Faria showed that the multiplicity of Laplacian eigenvalue 1 is greater than or
equal to the difference between the number of pendant vertices and the number
of quasi-pendant vertices. But if a graph has a pendant vertex, then it is at
most 1-connected. In this paper, we investigate a class of 2-connected
$k$-symmetric graphs with a Laplacian eigenvalue 1. We also identify a class of
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act freely on a graph $G$, then we say that $G$ is $k$-symmetric. In 1985,
Faria showed that the multiplicity of Laplacian eigenvalue 1 is greater than or
equal to the difference between the number of pendant vertices and the number
of quasi-pendant vertices. But if a graph has a pendant vertex, then it is at
most 1-connected. In this paper, we investigate a class of 2-connected
$k$-symmetric graphs with a Laplacian eigenvalue 1. We also identify a class of
$k$-symmetric graphs in which all Laplacian eigenvalues are integers.</abstract><doi>10.48550/arxiv.2211.11164</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Combinatorics |
| title | On the Laplacian spectrum of $k$-symmetric graphs |
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