Regular embeddings of Cartesian product graphs

It is proved in this paper that if a Cartesian power X n of a prime graph X (with respect to the Cartesian multiplication) has an orientable regular embedding, then X has an orientable regular embedding too; and if a graph with some extra conditions has orientable regular embeddings, then its Cartes...

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Bibliographic Details
Published inDiscrete mathematics Vol. 312; no. 2; pp. 258 - 264
Main Author Zhang, Jun-Yang
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 28.01.2012
Elsevier
Subjects
Algebra
Applied sciences
Cartesian
Cartesian product
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Exact sciences and technology
Graphs
Grid-like graph
Information retrieval. Graph
Mathematical analysis
Mathematics
Multiplication
Regular map
Sciences and techniques of general use
Theorems
Theoretical computing
Grid-like graph
Regular map
Cartesian product
Graph product
Multiplication
Grid pattern
Discrete mathematics
Combinatorics
Power
Regular graph
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Summary:It is proved in this paper that if a Cartesian power X n of a prime graph X (with respect to the Cartesian multiplication) has an orientable regular embedding, then X has an orientable regular embedding too; and if a graph with some extra conditions has orientable regular embeddings, then its Cartesian power also has. As an application of our main theorems, the regular embeddings of grid-like graphs are studied.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2011.09.001