Regular Maps of Graphs of Order 4p

作     者：Jin Xin ZHOU Yan Quan FENG 

作者机构：Department of MathematicsBeijing Jiaotong University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2012年第28卷第5期

页      面：989-1012页

核心收录：

学科分类：081603[工学-地图制图学与地理信息工程] 07[理学] 08[工学] 070503[理学-地图学与地理信息系统] 070104[理学-应用数学] 0705[理学-地理学] 0816[工学-测绘科学与技术] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China (Grant Nos. 10871021, 10901015) Fundamental Research Funds for the Central Universities (Grant No. 2011JBM127) 

主　　题：Regular map Cayley map algebraic map 2-cell embedding 

摘      要：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.