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International Journal of Mathematics and Mathematical Sciences
Volume 2007, Article ID 42892, 8 pages
Research Article

General Symmetric Starter of Orthogonal Double Covers of Complete Bipartite Graph

Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Minoufiya University, Minuf, Egypt

Received 22 September 2006; Revised 13 February 2007; Accepted 8 May 2007

Academic Editor: Dalibor Froncek

Copyright © 2007 R. A. El-Shanawany and M. Sh. Higazy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.