Integral Cayley graphs over dicyclic group
Integral Cayley graphs over dicyclic group
复制标题
双环群上的积分凯莱图
DOI：
10.1016/j.laa.2019.01.002
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发表时间：
2019
影响因子：
1.1
通讯作者：
Huang Hualin
中科院分区：
文献类型：
--
作者：
Cheng Tao;Feng Lihua;Huang Hualin
Harary和Schwenk提出了如何对整图进行分类的问题。本文主要研究一类非交换群--双循环群T4 n=< a，B| a 2 n= 1，a n= B 2，B− 1 a B= a− 1>，并考虑其对应的Cayley图.借助于它的特征标表，我们首先得到了T4 n上Cayley图是完整图的一个充要条件。然后利用图的布尔代数得到了T4 n上Cayley图完整性的几个简单的充分条件< a>。作为一个副产品，我们确定了几个无限族的连通整Cayley图在T4 n。最后，对素数p，完全确定了双圈群T4 p上的所有整Cayley图.
How to classify all the integral graphs is a challenging work as suggested by Harary and Schwenk. In this paper, we focus on one non-abelian group—the dicyclic group T 4 n=< a, b| a 2 n= 1, a n= b 2, b− 1 a b= a− 1>, and consider its corresponding Cayley graphs. With the help of its character table, we first obtain a necessary and sufficient condition for the integrality of Cayley graphs over T 4 n. Then we obtain several simple sufficient conditions for the integrality of Cayley graphs over T 4 n in terms of the Boolean algebra of< a>. As a byproduct, we determine a few infinite families of connected integral Cayley graphs over T 4 n. At last, for a prime p, we completely determine all integral Cayley graphs over the dicyclic group T 4 p.