Mao Linfan1; Liu Yanpei2; Tian Feng3
Source Publicationactamathematicasinicaenglishseries
AbstractA 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 F 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 F 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.
Document Type期刊论文
Recommended Citation
GB/T 7714
Mao Linfan,Liu Yanpei,Tian Feng. automorphismsofmapswithagivenunderlyinggraphandtheirapplicationtoenumeration[J]. actamathematicasinicaenglishseries,2005,21(2):225.
APA Mao Linfan,Liu Yanpei,&Tian Feng.(2005).automorphismsofmapswithagivenunderlyinggraphandtheirapplicationtoenumeration.actamathematicasinicaenglishseries,21(2),225.
MLA Mao Linfan,et al."automorphismsofmapswithagivenunderlyinggraphandtheirapplicationtoenumeration".actamathematicasinicaenglishseries 21.2(2005):225.
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