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International Journal of Mathematics and Mathematical Sciences
Volume 2013 (2013), Article ID 265136, 4 pages
http://dx.doi.org/10.1155/2013/265136
Research Article

On Cartesian Products of Orthogonal Double Covers

Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufiya University, Menouf 32952, Egypt

Received 9 December 2012; Revised 11 February 2013; Accepted 18 March 2013

Academic Editor: Ilya M. Spitkovsky

Copyright © 2013 R. El Shanawany et al. 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.

Abstract

Let be a graph on vertices and a collection of subgraphs of , one for each vertex, where is an orthogonal double cover (ODC) of if every edge of occurs in exactly two members of and any two members share an edge whenever the corresponding vertices are adjacent in and share no edges whenever the corresponding vertices are nonadjacent in . In this paper, we are concerned with the Cartesian product of symmetric starter vectors of orthogonal double covers of the complete bipartite graphs and using this method to construct ODCs by new disjoint unions of complete bipartite graphs.