论文信息 - The Structure of Automorphism Groups of Cayley Graphs and Maps

The Structure of Automorphism Groups of Cayley Graphs and Maps

The automorphism groups Aut(C(G, X)) and Aut(CM(G, X, p)) of a Cayley graph C(G, X) and a Cayley map CM(G, X, p) both contain an isomorphic copy of the underlying group G acting via left translations. In our paper, we show that both automorphism groups are rotary extensions of the group G by the stabilizer subgroup of the vertex 1G. We use this description to derive necessary and sufficient conditions to be satisfied by a finite group in order to be the (full) automorphism group of a Cayley graph or map and classify all the finite groups that can be represented as the (full) automorphism group of some Cayley graph or map.

Robert Jajcay | R. Jajcay

[1] Martin Skoviera,et al. Regular maps from Cayley graphs II antibalanced Cayley maps , 1994, Discret. Math..

[2] Robert Jajcay. On a New Product of Groups , 1994, Eur. J. Comb..

[3] Robert Jajcay. On a Construction of Infinite Families of Regular Cayley Maps , 1998, Comb..

[4] Lewis A. Nowitz,et al. Graphical regular representations of non-abelian groups. II. , 1972 .

[5] Gareth A. Jones,et al. Regular orientable imbeddings of complete graphs , 1985, J. Comb. Theory, Ser. B.

[6] H. Wielandt,et al. Finite Permutation Groups , 1964 .

[7] Robert Jajcay. Characterization and construction of Cayley graphs admitting regular Cayley maps , 1996, Discret. Math..

[8] Arthur T. White,et al. Permutation Groups and Combinatorial Structures , 1979 .

[9] Norman Biggs. Cayley maps and symmetrical maps , 1972 .

[10] Robert Jajcay,et al. Automorphism Groups of Cayley Maps , 1993, J. Comb. Theory, Ser. B.

[11] Wilfried Imrich,et al. On graphical regular representations of cyclic extensions of groups , 1974 .

[12] Martin Skoviera,et al. Regular maps from Cayley graphs, part 1: Balanced Cayley maps , 1992, Discret. Math..

[13] H. Weyl. Permutation Groups , 2022 .

[14] G. Jones,et al. Theory of Maps on Orientable Surfaces , 1978 .