论文标题
在广义双环组上的Cayley图上
On Cayley graphs over generalized dicyclic groups
论文作者
论文摘要
最近，许多作者的几项作品研究了在某些有限基团（例如Dicyclic组和（广义）二面体组）上Cayley图的完整性，距离的完整性和距离功率。我们的目的是概括和/或给出这些结果的类似物。例如，我们在广义双环组上为Cayley图提供了必要和充分的条件（即，其邻接矩阵的所有特征值均以$ \ mathbb {z} $为单位）。我们还获得了足够的条件，可以在给定的广义双环组上cayley图的所有距离功率的完整性。这些结果分别扩展了Cheng-feng-huang和cheng-feng-liu-lu- stevanovic对双环组的工作。
Recently, several works by a number of authors have studied integrality, distance integrality, and distance powers of Cayley graphs over some finite groups, such as dicyclic groups and (generalized) dihedral groups. Our aim is to generalize and/or to give analogues of these results for generalized dicyclic groups. For example, we give a necessary and sufficient condition for a Cayley graph over a generalized dicyclic group to be integral (i.e., all eigenvalues of its adjacency matrix are in $\mathbb{Z}$). We also obtain sufficient conditions for the integrality of all distance powers of a Cayley graph over a given generalized dicyclic group. These results extend works on dicyclic groups by Cheng--Feng--Huang and Cheng--Feng--Liu--Lu--Stevanovic, respectively.
