Cartesian product of two symmetric starter vectors of orthogonal double covers

An orthogonal double cover (ODC) of a graph HH is a collection G={Gv:v∈V(H)}G={Gv:v∈V(H)} of |V(H)||V(H)| subgraphs of HH such that every edge of HH is contained in exactly two members of GG and for any two members GuGu and GvGv in GG, |E(Gu)∩E(Gv)||E(Gu)∩E(Gv)| is 1 if uu and vv are adjacent in HH and it is 0 if uu and vv are nonadjacent in HH.In this paper, we are concerned with the Cartesian product of symmetric starter vectors of orthogonal double covers of the complete bipartite graphs and using this method to construct ODCs for new graph classes.