A Cayley map is a Cayley graph embedded in an orientable surface such that. the local rotations at every vertex are identical. In this paper, balanced regular Cayley maps for cyclic groups, dihedral groups, and genera...A Cayley map is a Cayley graph embedded in an orientable surface such that. the local rotations at every vertex are identical. In this paper, balanced regular Cayley maps for cyclic groups, dihedral groups, and generalized quaternion groups are classified.展开更多
A 2-cell embedding f ： X → S of a graph X into a closed orientable surface S can be described combinatorially by a pair M = （X; p） called a map, where p is a product of disjoint cycle permutations each of which is...A 2-cell embedding f ： X → S of a graph X into a closed orientable surface S can be described combinatorially by a pair M = （X; p） called a map, where p is a product of disjoint cycle permutations each of which is the permutation of the arc set of X initiated at the same vertex following the orientation of S. It is well known that the automorphism group of M acts semi-regularly on the arc set of X and if the action is regular, then the map M and the embedding f are called regular. Let p and q be primes. Duet al. [J. Algebraic Combin., 19, 123 141 （2004）] classified the regular maps of graphs of order pq. In this paper all pairwise non-isomorphic regular maps of graphs of order 4p are constructed explicitly and the genera of such regular maps are computed. As a result, there are twelve sporadic and six infinite families of regular maps of graphs of order 4p; two of the infinite families are regular maps with the complete bipartite graphs K2p,2p as underlying graphs and the other four infinite families are regular balanced Cayley maps on the groups Z4p, Z22 × Zp and D4p.展开更多
基金Supported by NSF of China(No.10001005) and Com~2MaC-KOSEF
文摘A Cayley map is a Cayley graph embedded in an orientable surface such that. the local rotations at every vertex are identical. In this paper, balanced regular Cayley maps for cyclic groups, dihedral groups, and generalized quaternion groups are classified.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10871021, 10901015)Fundamental Research Funds for the Central Universities (Grant No. 2011JBM127)
文摘A 2-cell embedding f ： X → S of a graph X into a closed orientable surface S can be described combinatorially by a pair M = （X; p） called a map, where p is a product of disjoint cycle permutations each of which is the permutation of the arc set of X initiated at the same vertex following the orientation of S. It is well known that the automorphism group of M acts semi-regularly on the arc set of X and if the action is regular, then the map M and the embedding f are called regular. Let p and q be primes. Duet al. [J. Algebraic Combin., 19, 123 141 （2004）] classified the regular maps of graphs of order pq. In this paper all pairwise non-isomorphic regular maps of graphs of order 4p are constructed explicitly and the genera of such regular maps are computed. As a result, there are twelve sporadic and six infinite families of regular maps of graphs of order 4p; two of the infinite families are regular maps with the complete bipartite graphs K2p,2p as underlying graphs and the other four infinite families are regular balanced Cayley maps on the groups Z4p, Z22 × Zp and D4p.
