Circular Intensely Orthogonal Double Cover Design of Balanced Complete Multipartite Graphs.

In this paper, we generalize the orthogonal double covers (ODC) of K n , n as follows. The circular intensely orthogonal double cover design (CIODCD) of X = K n , n , ... , n ︸ m is defined as a collection T = { G 0 0 , G 1 0 , ... , G (n − 1) 0 } ∪ { G 0 1 , G 1 1 , ... , G (n − 1) 1 } of isomorphic spanning subgraphs of X such that every edge of X appears twice in the collection T , E (G i 0 ) ∩ E (G j 0 ) = E (G i 1 ) ∩ E (G j 1 ) = 0 , i ≠ j and   E (G i 0 ) ∩ E (G j 1 ) = λ = m 2 , i , j ∈ ℤ n. 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. [ABSTRACT FROM AUTHOR]