Automorphisms of maps with a given underlying graph and their application to enumeration

doi:10.1007/s10114-004-0494-0

	Automorphisms of maps with a given underlying graph and their application to enumeration
	Mao, LF ; Liu, YP ; Tian, F
刊名	ACTA MATHEMATICA SINICA-ENGLISH SERIES
	2005-04-01
卷号	21 期号:2 页码:225-236
关键词	embedding map Cayley graph circulant graph symmetric graph automorphism group Burnside Lemma
ISSN号	1439-8516
DOI	10.1007/s10114-004-0494-0
英文摘要	A graph is called a semi-regular graph if its automorphism group action on its ordered pair of adjacent vertices is semi-regular. In this paper, a necessary and sufficient condition for an automorphism of the graph F to be an automorphism of a map with the underlying graph G is obtained. Using this result, all orientation-preserving automorphisms of maps on surfaces (orientable and non-orientable) or just orientable surfaces with a given underlying semi-regular graph G are determined. Formulas for the numbers of non-equivalent embeddings of this kind of graphs on surfaces (orientable, non-orientable or both) are established, and especially, the non-equivalent embeddings of circulant graphs of a prime order on orientable, non-orientable and general surfaces are enumerated.
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000228979100001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/1179]
专题	中国科学院数学与系统科学研究院
通讯作者	Mao, LF
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Beijing Jiaotong Univ, Inst Appl Math, Beijing 100044, Peoples R China
推荐引用方式 GB/T 7714	Mao, LF,Liu, YP,Tian, F. Automorphisms of maps with a given underlying graph and their application to enumeration[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2005,21(2):225-236.
APA	Mao, LF,Liu, YP,&Tian, F.(2005).Automorphisms of maps with a given underlying graph and their application to enumeration.ACTA MATHEMATICA SINICA-ENGLISH SERIES,21(2),225-236.
MLA	Mao, LF,et al."Automorphisms of maps with a given underlying graph and their application to enumeration".ACTA MATHEMATICA SINICA-ENGLISH SERIES 21.2(2005):225-236.