论文标题
在$ k $ -smmetric图的拉普拉斯频谱上
On the Laplacian spectrum of $k$-symmetric graphs
论文作者
论文摘要
对于某些正整数$ k $，如果有限的循环组$ \ mathbb {z} _k $可以自由地在图$ g $上行动，那么我们说$ g $是$ k $ - symmetric。 1985年，法里亚（Faria）表明，拉普拉斯特征值1的多样性大于或等于吊坠顶点数量和准吊式顶点数量之间的差异。但是，如果图具有吊坠顶点，则最多是1连接的。在本文中，我们研究了带有laplacian特征值1的2个连接的$ k $对称图。我们还确定了所有laplacian eigenvalues is integers的$ k $ symmetric图。
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.
