Generalization of the Symmetric Starter of the Orthogonal Double Covers of the Complete Bipartite Graph
El-Serafi, S., El-Shanawany, R., Higazy, M. (2006). Generalization of the Symmetric Starter of the Orthogonal Double Covers of the Complete Bipartite Graph. EKB Journal Management System, 16(2), 171-177. doi: 10.21608/mjeer.2006.64856
S. A. El-Serafi; R. A. El-Shanawany; M. Sh. Higazy. "Generalization of the Symmetric Starter of the Orthogonal Double Covers of the Complete Bipartite Graph". EKB Journal Management System, 16, 2, 2006, 171-177. doi: 10.21608/mjeer.2006.64856
El-Serafi, S., El-Shanawany, R., Higazy, M. (2006). 'Generalization of the Symmetric Starter of the Orthogonal Double Covers of the Complete Bipartite Graph', EKB Journal Management System, 16(2), pp. 171-177. doi: 10.21608/mjeer.2006.64856
El-Serafi, S., El-Shanawany, R., Higazy, M. Generalization of the Symmetric Starter of the Orthogonal Double Covers of the Complete Bipartite Graph. EKB Journal Management System, 2006; 16(2): 171-177. doi: 10.21608/mjeer.2006.64856

Generalization of the Symmetric Starter of the Orthogonal Double Covers of the Complete Bipartite Graph

Menoufia Journal of Electronic Engineering Research
Article 3, Volume 16, Issue 2, July 2006, Page 171-177  XML
Document Type: Original Article
DOI: 10.21608/mjeer.2006.64856
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Authors
S. A. El-Serafi1; R. A. El-Shanawany1; M. Sh. Higazy2
1Department of Physics and Engineering Mathematics, Faculty Of Electronic Engineering, Minoufiya University, Minuf, Egypt
2Department of Physics and Engineering Mathematics, Faculty Of Electronic Engineering, Minoufiya University, Minuf, Egypt.
Abstract
An Orthogonal Double Cover of the complete graph is a set 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 have constructed the ODC of the complete bipartite graph (), for any values of , and all graphs in the collection are isomorphic to the spanning sub-graph
Keywords
Orthogonal double cover; ODC; Graph decompositions; Symmetric starter
References
[1]      B. Ganter, H.-D.O.F. Gronau, R. C. Mullin, ”On orthogonal double covers of ”, Ars Combin. 37 (1994) 209-221.

[2]     B. Ganter, H.-D.O.F. Gronau, ”On two conjectures of Demetrovics, Füredi and Katona on partitions”, Discrete Math. 88 (1991) 194-155.

[3]     [3] F. E. Bennet, L. Wu, ”On minimum matrix representation of closure operations”, Discrete Appl. Math. 26 (1990) 25-40.

[4]     H.-D.O.F. Gronau, S. Hartman, M. Grüttmüller, U. Leck, V. Leck, ”On orthogonal double covers of graphs”, Design Codes Cryptography 27 (2002) 49-91.

[5]     H.-D.O.F. Gronau, R.C. Mullin, A. Rosa, ”Orthogonal double covers of complete graphs by trees”, Graphs Combin. 13 (1997) 251-262.

[6]     R. El-Shanawany, Hans-Dietrich O.F. Gronau, and Martin Grüttmüller. ”Orthogonal Double Covers of  by Small Graphs”, Discrete Applied Mathematics 138 (2004) 47-63.

[7]     R. El-shanwany, ”Orthogonal Double Covers of Complete Bipartite Graphs”, Ph.D. Thesis, Universität Rostock, 2002.

[8]     [8] El-Serafi Said A., El-Shanawany Ramadan A., Higazy Mahmoud Sh., ”Orthogonal Double Covers of  by The Union of  with Connected ” , MJEER, Vol. 15, No. 1, January 2005.

[9]     S. Hartmann, U. Leck, V. Leck, A conjecture on orthogonal double covers by paths, Congr. Numer. 140 (1999) 187-193.

[10] V. Leck, ”Orthogonal double covers of ”, Ph.D. Thesis, Universtät rostock, 2002.

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