Heawood图的s-正则循环覆盖分类  

Classification of s-Regular Cyclic Coverings of Heawood Graph

作　　者：刘志强[1] 李文汉[2] 

机构地区：[1]北京建筑工程学院理学院,北京100044 [2]石家庄经济学院数理学院,石家庄050031

出　　处：《河南师范大学学报（自然科学版）》2012年第2期15-18,共4页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(10071002);河北省教育厅科研项目(Z2010297);北京建筑工程学院教研科研项目(Y10-25;Z07052)

摘　　要：一个图称为s-正则的,如果它的自同构群作用在它的s-弧集上是正则的.运用电压图及提升理论,对Heawood图的循环覆盖进行了分类.证明了:Heawood图的循环覆盖是1-正则的或2-正则的,当循环群的阶数不等于7或21时,覆盖是1-正则的,并且给出了这个1-正则无限类的构造;当循环群的阶数等于7或21时,覆盖是2-正则的.A graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. By theoriems of voltage graph and lifts s-regular cyclic coverings of the Heawood graph are classified. It has been proved that the cyclic coverings of heawood are 1-regular graphs or 2-regular graphs, if the orders of cyclic group are not equel to 7 or 21, then the coverings are 1-regular;if the orders of cyclic group are equel to 7 or 21 ,then the coverings are 2-regular.

关 键 词：S-正则图 s-弧-传递图 正则覆盖 

分 类 号：O157.5[理学—数学] O152.9[理学—基础数学]