## Abstract In this paper, it will be shown that the isomorphism classes of regular orientable embeddings of the complete bipartite graph __K__~__n,n__~ are in oneβtoβone correspondence with the permutations on __n__ elements satisfying a given criterion, and the isomorphism classes of them are com
On the orientable regular embeddings of complete multipartite graphs
β Scribed by Jun-Yang Zhang; Shao-Fei Du
- Book ID
- 113582504
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 251 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0195-6698
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π SIMILAR VOLUMES
In this paper we consider those 2-cell orientable embeddings of a complete graph K n+1 which are generated by rotation schemes on an abelian group 8 of order n+1, where a rotation scheme an 8 is defined as a cyclic permutation ( ; 1 , ; 2 , ..., ; n ) of all nonzero elements of 8. It is shown that t
## Abstract In this paper we examine selfβdual embeddings of complete multipartite graphs, focusing primarily on __K__~__m__(__n__)~ having __m__ parts each of size __n.__ If __m__ = 2, then __n__ must be even. If the embedding is on an orientable surface, then an Euler characteristic argument show
In this paper, we study the achromatic indices of the regular complete multipartite graphs and obtain the following results: (1) A good upper bound for the achromatic index of the regular complete multipartite graph which gives the exact values of an infinite family of graphs and solves a problem p
A subgraph H of a graph G is called a star-subgraph if each component of H is a star. The star-arboricify of G, denoted by sa(G), is the minimum number of star-subgraphs that partition the edges of G. In this paper we show that sa(G) is [r/21 + 1 or [r/2] + 2 for the complete r-regular multipartite