Orthogonal double covers of 4-regular circulant graphs

An orthogonal double cover (ODC) of a graph H is a collection g = {G(v) : v is an element of V(H)} of vertical bar V(H)vertical bar 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, vertical bar E(G(u)) boolean AND E(Gu)vertical bar 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 if the cyclic group of order vertical bar V(H)vertical bar is a subgroup of the automorphism group of 0; otherwise it is noncyclic. Recently, Sampathkumar and Srinivasan settled the problem of the existence of cyclic ODCs of 4-regular circulant graphs. In this paper, we are concerned with noncyclic ODCs of such graphs, whenever a cyclic ODC does not exist.