Enumeration of cubic Cayley graphs on dihedral groups

被引：0
作者：
Xue Yi Huang
Qiong Xiang Huang
Lu Lu
机构：
[1] Xinjiang University,College of Mathematics and Systems Science
来源：
Acta Mathematica Sinica, English Series | 2017年 / 33卷
关键词：
Cayley graph; dihedral group; cospectral; isomorphic classes; quadratic reciprocity; 05C25; 05C50;
D O I：
暂无
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学科分类号：
摘要：
Let p be an odd prime, and D2p = 〈a, b | ap = b2 = 1, bab = a−1〉 the dihedral group of order 2p. In this paper, we completely classify the cubic Cayley graphs on D2p up to isomorphism by means of spectral method. By the way, we show that two cubic Cayley graphs on D2p are isomorphic if and only if they are cospectral. Moreover, we obtain the number of isomorphic classes of cubic Cayley graphs on D2p by using Gauss’ celebrated law of quadratic reciprocity.
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页码：996 / 1010
页数：14
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