General Symmetric Starter of Orthogonal Double Covers of Complete Bipartite Graph
An orthogonal double cover (ODC) of the complete graph is a collection of graphs such that every two of them share exactly one edge and every edge of the complete graph belongs to exactly two of the graphs. In this paper, we consider the case where the graph to be covered twice is the complete bipar...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/42892 |
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| author | R. A. El-Shanawany M. Sh. Higazy |
| author_facet | R. A. El-Shanawany M. Sh. Higazy |
| author_sort | R. A. El-Shanawany |
| collection | DOAJ |
| description | An orthogonal double cover (ODC) of the complete graph is a collection of graphs such that every two of them share exactly one edge and every edge of the complete graph belongs to exactly two of the graphs. In this paper, we consider the case where the graph to be covered twice is the complete bipartite graph Kmn,mn (for any values of m,n) and all graphs in the collection are isomorphic to certain spanning subgraphs. Furthermore, the ODCs of Kn,n by certain disjoint stars are constructed. |
| format | Article |
| id | doaj-art-fee6e290a529497aa873c712e088a31e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fee6e290a529497aa873c712e088a31e2025-02-03T01:11:26ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/4289242892General Symmetric Starter of Orthogonal Double Covers of Complete Bipartite GraphR. A. El-Shanawany0M. Sh. Higazy1Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Minoufiya University, Minuf, EgyptDepartment of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Minoufiya University, Minuf, EgyptAn orthogonal double cover (ODC) of the complete graph is a collection of graphs such that every two of them share exactly one edge and every edge of the complete graph belongs to exactly two of the graphs. In this paper, we consider the case where the graph to be covered twice is the complete bipartite graph Kmn,mn (for any values of m,n) and all graphs in the collection are isomorphic to certain spanning subgraphs. Furthermore, the ODCs of Kn,n by certain disjoint stars are constructed.http://dx.doi.org/10.1155/2007/42892 |
| spellingShingle | R. A. El-Shanawany M. Sh. Higazy General Symmetric Starter of Orthogonal Double Covers of Complete Bipartite Graph International Journal of Mathematics and Mathematical Sciences |
| title | General Symmetric Starter of Orthogonal Double Covers of Complete Bipartite Graph |
| title_full | General Symmetric Starter of Orthogonal Double Covers of Complete Bipartite Graph |
| title_fullStr | General Symmetric Starter of Orthogonal Double Covers of Complete Bipartite Graph |
| title_full_unstemmed | General Symmetric Starter of Orthogonal Double Covers of Complete Bipartite Graph |
| title_short | General Symmetric Starter of Orthogonal Double Covers of Complete Bipartite Graph |
| title_sort | general symmetric starter of orthogonal double covers of complete bipartite graph |
| url | http://dx.doi.org/10.1155/2007/42892 |
| work_keys_str_mv | AT raelshanawany generalsymmetricstarteroforthogonaldoublecoversofcompletebipartitegraph AT mshhigazy generalsymmetricstarteroforthogonaldoublecoversofcompletebipartitegraph |