On the one edge algorithm for the orthogonal double covers
Prikladnaâ diskretnaâ matematika, no. 3 (2019), pp. 78-84.

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The existing problem of the orthogonal double covers of the graphs is well-known in the theory of combinatorial designs. In this paper, a new technique called the one edge algorithm for constructing the orthogonal double covers of the complete bipartite graphs by copies of a graph is introduced. The advantage of this algorithm is that it is accessible to discrete mathematicians not intimately familiar with the theory of the orthogonal double covers.
Keywords: symmetric starter, orthogonal double covers.
Mots-clés : graph decomposition
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R. El-Shanawany; A. El-Mesady. On the one edge algorithm for the orthogonal double covers. Prikladnaâ diskretnaâ matematika, no. 3 (2019), pp. 78-84. http://geodesic.mathdoc.fr/item/PDM_2019_3_a8/

[1] Demetrovics J., Füredi Z., Katona G. O. H., “Minimum matrix representations of closure operations”, Discrete Appl. Math., 1985, no. 11, 115–128 | DOI | MR | Zbl

[2] Demetrovics J., Katona G. O. H., “External combinatorial problems in relational database”, Fundamentals of Combinatorics of Computation Theory, Springer, Berlin, 1981, 110–119 | DOI

[3] Alspach B., Heinrich K., Liu G., “Orthogonal factorizations of graphs”, Contemporary Design Theory, ch. 2, eds. J. H. Dinitz, D. R. Stinson, Wiley, N.Y., 1992 | MR

[4] Heinrich K., “Graph decompositions and designs”, CRC Handbook of Combinatorial Designs, ch. IV.22, eds. C. J. Colbourn, J. H. Dinitz, CRC Press, Boca Raton, 1996 | MR | Zbl

[5] Scapellato R., El-Shanawany R., Higazy M., “Orthogonal double covers of Cayley graphs”, Discrete Appl. Math., 157 (2009), 3111–3118 | DOI | MR | Zbl

[6] El-Shanawany R., Higazy M., Shabana H., El-Mesady A., “Cartesian product of two symmetric starter vectors of orthogonal double covers”, AKCE Intern. J. Graphs and Combinatorics, 2015, no. 12, 59–63 | DOI | MR | Zbl

[7] Gronau H.-D. O. F., Hartman S., Grüttmüller M., et al., “On orthogonal double covers of graphs”, Design Codes Cryptography, 27 (2002), 49–91 | DOI | MR | Zbl

[8] El-Shanawany R., Gronau H.-D. O. F., Grüttmüller M., “Orthogonal double covers of $K_{n,n}$ by small graphs”, Discrete Appl. Math., 138 (2004), 47–63 | DOI | MR | Zbl

[9] El-Serafi S., El-Shanawany R., Shabana H., “Orthogonal double cover of complete bipartite graph by disjoint union of complete bipartite graphs”, Ain Shams Engineering J., 2015, no. 6, 657–660 | DOI

[10] Sampathkumar R., Srinivasan S., “Cyclic orthogonal double covers of 4-regular circulant graphs”, Discr. Math., 311 (2011), 2417– 2422 | DOI | MR | Zbl

[11] El-Shanawany R., Higazy M., El-Mesady A., “On cartesian products of orthogonal double covers”, Intern. J. Math. and Math. Sci., 2013 (2013), 265136, 4 pp. | DOI | MR | Zbl

[12] Froncek D., “Orthogonal double covers of complete graphs by lobsters of diameter 4”, Congr. Numer., 177 (2005), 25–32 | MR | Zbl