A graph \(\varGamma \) is called n-Cayley graph over a group G if \(\mathrm{Aut}(\varGamma )\) has a semiregular subgroup isomorphic to G with n orbits (of equal size). In this paper, we give a decomposition of the Laplacian and signless Laplacian polynomials of n-Cayley graphs in terms of irreducible representations of G. Also, we construct several families of graphs with integral Laplacian and signless Laplacian spectrum.

中文翻译：

---

具有半规则自同构图的Laplacian和无符号Laplacian多项式

的曲线图\（\ varGamma \）被称为Ñ在一组-Cayley图表ģ如果\（\ mathrm {AUT}（\ varGamma）\）具有半规则子组同构ģ与Ñ轨道（大小相等）。在本文中，我们用G的不可约表示来分解n -Cayley图的Laplacian和无符号Laplacian多项式。此外，我们构造了带有积分拉普拉斯谱和无符号拉普拉斯谱的图族。