General Cyclic Orthogonal Double Covers of Finite Regular Circulant Graphs

An orthogonal double cover (ODC) of a graph H is a collection ( ) { } v G v V H : = ∈  of ( ) V H subgraphs (pages) of H, so that they cover every edge of H twice and the intersection of any two of them contains exactly one edge. An ODC  of H is cyclic (CODC) if the cyclic group of order ( ) V H is a subgroup of the automorphism group of  . In this paper, we introduce a general orthogonal labelling for CODC of circulant graphs and construct CODC by certain classes of graphs such as complete bipartite graph, the union of the co-cycles graph with a star, the center vertex of which, belongs to the co-cycles graph and graphs that are connected by a one vertex.