Orthogonal double cover of Complete Bipartite Graph by disjoint union of complete bipartite graphs

Abstract

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