Cyclic orthogonal double covers of 4-regular circulant graphs

An orthogonal double cover (ODC) of a graph H is a collection G = { G v : v ∈ V ( H ) } of | V ( H ) | subgraphs of H such that every edge of H is contained in exactly two members of G and for any two members G u and G v in G , | E ( G u ) ∩ E ( G v ) | is 1 if u and v are adjacent in H and it is 0 if u and v are nonadjacent in H . An ODC G of H is cyclic (CODC) if the cyclic group of order | V ( H ) | is a subgroup of the automorphism group of G . In this paper, we are concerned with CODCs of 4-regular circulant graphs.