Circular Intensely Orthogonal Double Cover Design of Balanced Complete Multipartite Graphs

In this paper, we generalize the orthogonal double covers (ODC) of Kn,n as follows. The circular intensely orthogonal double cover design (CIODCD) of X=Kn,n,…,n︸m is defined as a collection T={G00,G10,…,G(n−1)0}∪{G01,G11,…,G(n−1)1} of isomorphic spanning subgraphs of X such that every edge of X appears twice in the collection T,E(Gi0)∩E(Gj0)=E(Gi1)∩E(Gj1)=0,i≠jand E(Gi0)∩E(Gj1)=λ=m2,i,j∈ℤn. We define the half starters and the symmetric starters matrices as constructing methods for the CIODCD of X. Then, we introduce some results as a direct application to the construction of CIODCD of X by the symmetric starters matrices.