On the isomorphisms and automorphism groups of circulants |
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Authors: | Qiongxiang Huang Jixiang Meng |
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Institution: | (1) Department of Mathematics of Xinjiang University, 830046 Xinjiang Urumuqi, P.R. China |
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Abstract: | Denote byC
n(S) the circulant graph (or digraph). LetM be a minimal generating element subset ofZ
n, the cyclic group of integers modulon, and
In this paper, we discuss the problems about the automorphism group and isomorphisms ofC
n(S). When M
S
, we determine the automorphism group ofC
n(S) and prove that for any T
if and only ifT = S, where is an integer relatively prime ton. The automorphism groups and isomorphisms of some other types of circulant graphs (or digraphs) are also considered. In the last section of this paper, we give a relation between the isomorphisms and the automorphism groups of circulants. |
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Keywords: | |
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