Congruence classes of orientable 2-cell embeddings of bouquets of circles and dipoles
SCIE
SCOPUS
- Title
- Congruence classes of orientable 2-cell embeddings of bouquets of circles and dipoles
- Authors
- Feng, YQ; Kwak, JH; Zhou, JX
- Date Issued
- 2010-03-08
- Publisher
- ELECTRONIC JOURNAL OF COMBINATORICS
- Abstract
- Two 2-cell embeddings i : X -> S and j : X -> S of a connected graph X into a closed orientable surface S are congruent if there are an orientation-preserving surface homeomorphism h : S -> S and a graph automorphism gamma of X such that ih = gamma j. Mull et al. [Proc. Amer. Math. Soc. 103(1988) 321 330] developed an approach for enumerating the congruence classes of 2-cell embeddings of a simple graph (without loops and multiple edges) into closed orientable surfaces and as an application, two formulae of such enumeration were given for complete graphs and wheel graphs. The approach was further developed by Mull [J. Graph Theory 30(1999) 77-90] to obtain a formula for enumerating the congruence classes of 2-cell embeddings of complete bipartite graphs into closed orientable surfaces. By considering automorphisms of a graph as permutations on its dart set, in this paper Mull et al.'s approach is generalized to any graph with loops or multiple edges, and by using this method we enumerate the congruence classes of 2-cell embeddings of a bouquet of circles and a dipole into closed orientable surfaces.
- Keywords
- COMPLETE GRAPHS; IMBEDDINGS; DISTRIBUTIONS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/26355
- DOI
- 10.37236/313
- ISSN
- 1077-8926
- Article Type
- Article
- Citation
- ELECTRONIC JOURNAL OF COMBINATORICS, vol. 17, no. 1, 2010-03-08
- Files in This Item:
- There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.