On the Automorphism Groups of Bi-Cayley Graphs

Acta Scientiarum Naturalium Universitatis Pekinensis

On the Automorphism Groups of Bi-Cayley Graphs

LU Zaiping

School of Mathematical Sciences, Peking University, Beijing, 100871

Received:2002-01-11 Online:2003-01-20 Published:2003-01-20

双Cayley图的自同构群

路在平

北京大学数学科学学院，北京，100871

Abstract

Abstract: For a finite group G, and a subset S(possibly, contains the identity element) of G, the bi-Cayley graph BCay(G, S) of G with respect to S is defined as the bipartite graph with vertex set G×{0, 1} and edge set {{(g, 0), (sg, 1)}|g∈G, s∈S}. The automorphism group A of bi-Cayley graph BCay(G, S) is investigated, and the structure of N_A(R^r_l(G)) is given.

Key words: edge transitive graph, semisymmetric graph, Cayley graph, bi-Cayley graph

摘要： 设G是有限群，S是G的一个子集(可能含有单位元)。群G关于S的双Cayley图BCay(G,S)是以G×{0,1}为点集而以{{(g,0),( sg,1)}| g∈G,s∈S}为边集的二部图。考查了双Cayley图BCay(G,S)的自同构群A，并决定了N_A (R^r_l(G))的结构。

关键词: 边传递图, 半对称图, Cayley图, 双Cayley图

CLC Number:

O157

LU Zaiping. On the Automorphism Groups of Bi-Cayley Graphs[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

路在平. 双Cayley图的自同构群[J]. 北京大学学报（自然科学版）.

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