The semi-arc automorphism group of a graph with application to map enumeration

doi:10.1007/s00373-006-0637-4

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	The semi-arc automorphism group of a graph with application to map enumeration
	Mao, LF ; Liu, YP ; Wei, EL
	2006-04-01
发表期刊	GRAPHS AND COMBINATORICS
ISSN	0911-0119
卷号	22 期号:1 页码:83-101
摘要	A map is a connected topological graph cellularly embedded in a surface. For a given graph Gamma, its genus distribution of rooted maps and embeddings on orientable and non-orientable surfaces are separately investigated by many researchers. By introducing the concept of a semi-arc automorphism group of a graph and classifying all its embeddings under the action of its semi-arc automorphism group, we find the relations between its genus distribution of rooted maps and genus distribution of embeddings on orientable and non-orientable surfaces, and give some new formulas for the number of rooted maps on a given orientable surface with underlying graph a bouquet of cycles B-n, a closed-end ladder L-n or a Ringel ladder R-n. A general scheme for enumerating unrooted maps on surfaces(orientable or non-orientable) with a given underlying graph is established. Using this scheme, we obtained the closed formulas for the numbers of non-isomorphic maps on orientable or non-orientable surfaces with an underlying bouquet B-n in this paper.
关键词	embedding map semi-arc automorphism group burnside lemma
DOI	10.1007/s00373-006-0637-4
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000237191200006
出版者	SPRINGER TOKYO
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2412
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, Beijing 100080, Peoples R China 2.No Jiaotong UNiv, Inst Appl Math, Beijing 100044, Peoples R China 3.Renmin Univ China, Informat Sch, Beijing 100872, Peoples R China
推荐引用方式 GB/T 7714	Mao, LF,Liu, YP,Wei, EL. The semi-arc automorphism group of a graph with application to map enumeration[J]. GRAPHS AND COMBINATORICS,2006,22(1):83-101.
APA	Mao, LF,Liu, YP,&Wei, EL.(2006).The semi-arc automorphism group of a graph with application to map enumeration.GRAPHS AND COMBINATORICS,22(1),83-101.
MLA	Mao, LF,et al."The semi-arc automorphism group of a graph with application to map enumeration".GRAPHS AND COMBINATORICS 22.1(2006):83-101.