论文信息 - Regular embeddings of Cartesian product graphs

Regular embeddings of Cartesian product graphs

It is proved in this paper that if a Cartesian power X^n of a prime graph X (with respect to the Cartesian multiplication) has an orientable regular embedding, then X has an orientable regular embedding too; and if a graph with some extra conditions has orientable regular embeddings, then its Cartesian power also has. As an application of our main theorems, the regular embeddings of grid-like graphs are studied.

Jun-Yang Zhang

[1] J. Dixon,et al. Permutation Groups , 1996 .

[2] Jozef Širáň,et al. Characterisation of Graphs which Underlie Regular Maps on Closed Surfaces , 1999 .

[3] Wilfried Imrich,et al. Topics in Graph Theory: Graphs and Their Cartesian Product , 2008 .

[4] Gareth A. Jones,et al. Classification and Galois conjugacy of Hamming maps , 2010, Ars Math. Contemp..

[5] H. Coxeter,et al. Generators and relations for discrete groups , 1957 .

[6] N. Biggs. Algebraic Graph Theory , 1974 .

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