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