CYCLIC ORTHOGONAL DOUBLE COVERS OF 6-REGULAR CIRCULANT GRAPHS BY DISCONNECTED FORESTS

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(G(v)) 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 G; otherwise it is noncyclic. Recently, Sampathkumar and Srinivasan settled the problem of the existence of cyclic ODCs of 4-regular circulant graphs. An ODC G of H is cyclic (CODC) if the cyclic group of order vertical bar V (H) vertical bar is a subgroup of the automorphism group of G, the set of all automorphisms of G; otherwise it is noncyclic. In this paper, we have completely settled the existence problem of CODCs of 6-regular circulant graphs by four acyclic disconnected graphs.