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.