Orthogonal Double Covers of Complete Bipartite Graphs by Certain Disjoint Union Cyclic Graphs
R. El-Shanawany
Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf, Egypt.
E. El-Kholy
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.
T. Homoda
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.
Z. Bakr *
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.
*Author to whom correspondence should be addressed.
Abstract
Let kn,n be a complete bipartite graph on 2n vertices and G be a collection of 2n subgraphs of kn,n.G is said to be an orthogonal double cover (ODC) of kn,n if every edge of kn,n is contained in exactly two members of G and any two members share an edge whenever the corresponding vertices are adjacent in kn,n and share no edges whenever the corresponding vertices are non-adjacent in kn,n, and all subgraphs in G are isomorphic to a given subgraph G of kn,n. Our aim in this paper gets an ODC of kn,n by ∪Cs;s≤n, and we construct large (ODCs) of kn,n by ∪(αCs); where m=αn;α∈Z+.
Keywords: Ecotypes of Anthephora, Graph decomposition, iations in mineral reqire, orthogonal double covers, symmetric starter, G-squares
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References
Demetrovics J, Füredi Z, Katona GOH. Minimum matrix representations of closure operations. Discrete appl. Math. 1985;11:115-128.
Hering F, Rosenfeld M. Problem number 38. In K. Heinrich, editor, Unsolved problems: Summer research workshop in algebraic combinatorics. Simon Fraser University; 1979.
Ganter B, Gronau HDOF, Mullin RC. On orthogonal double covers of K_n. Ars Combinatoria. 1994; 37:209-221 .
Ganter B, Gronau HDOF. Two conjectures of Demetrovics, Füredi, and Katona, concerning Partitions. Discrete Mathematics. 1991;88(2-3): 149-155.
Gronau HDOF, Mullin RC, Rosa A. Orthogonal double covers of complete graphs by trees. Graphs and Combinatorics. 1997;13(3):251-262.
El-Shanawany R, Gronau HDOF, Grüttmüller M. Orthogonal Doubl Covers of K_(n,n) by small graphs. Discrete Appl. Math. 2004;138:47-63.
Gronau HDOF, Grüttmüller M, Hartmann S, Leck U, Leck V. On orthogonal double covers of graphs. Designs, Codes and Cryptography. 2002;27(1-2):49-91.
El-Shanawany RA, Gronau HDOF, Grüttmüller M. Orthogonal double covers of K_(n,n) by small graphs. Discrete Appl. Math. 2004;138,47-63.
El-Shanawany RA. Orthogonal double covers of complete bipartite graphs. Ph. D. thesis, Universität Rostock, Germany; 2002.
El-Shanawany RA, El-Kholy E, Homoda T, Bakr Z. Orthogonal double covers of complete bipartite graphs by certain copies of cyclic and one factorization graphs. 2st International Conference on Electronic Engineering, Menoufia University, Egypt, ICEEM2021, 3-4 July 2021, 978-0-7381-2554-1/21/$31.00 (c) 2021 IEEE.
MaNeish HF. Euler squares. Ann. Math (NY). 1922;23:221-227.