Orthogonal Double Covers of Complete Bipartite Graphs by Certain Copies of Cyclic and one Factorization Graphs

Abstract

Let Kn,n be a complete bipartite graph on 2n vertices and G be a collection of 2n subgraphs of Kn,n, then G is an orthogonal double cover (ODC) of Kn,n if every edge of Kn,n exists in exactly two members of G and any two members of G share exactly an edge. If all subgraphs in G are isomorphic to a given subgraph G, then G is said to be an ODC of Kn,n by G. Our aim is to get an ODC of Kn,n by ∪Cs; s < n, and we will make extension for this ODC to get another one of Km,m by ∪(αCs); where m = αn; α ∈ Z⁺.