Orthogonal double covers of complete bipartite graphs by the union of a cycle and a star

Abstract Let H be a graph on n vertices and G a collection of n subgraphs of H, one for each vertex. Then 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 of G share exactly an edge whenever the corresponding vertices are adjacent in H. If all subgraphs in G are isomorphic to a given spanning subgraph G, then G is said to be an ODC of H by G. We construct ODCs of H = Kn,n by G = Cm ∪v Sn−m (union of a cycle Cm and a star Sn−m whose center vertex v belongs to that cycle and m = 6, 8, 10, 12 and m < n). Furthermore, we construct ODCs of H = Kn,n by G = Cm∪Sn−m (disjoint union of a cycle and a star) where m = 4, 8 and m < n. In all cases, G is a symmetric starter of the cyclic group of order n. In addition, we introduce a generalization of this result.