Abstract
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.
Highlights
In this paper, we are concerned with the finite, undirected, and simple graphs
The orthogonal double covers (ODC) are very important in solving many problems in the statistical design and Armsmtrong databases, the generalization of the ODCs to the circular intensely orthogonal double cover design (CIODCD) has a very important role in the statistical design theory and the relational databases
The ODC can be considered as a special case of our generalization
Summary
Received: 29 September 2020; Accepted: 19 OctoDbeefirni2ti0o2n01;. PThuebcolimsphleetde m: u2l1tipOarctitteogbreaprh2K0a21,.0..,am is the simple graph on n =. The set of vertices is partitioned into m parts of cardinalities a1, a2, . Am; an edge joins two vertices if and only if they The set of vertices is partitioned into m parts of cardinalities a1, a2, . . . , am; an edge joins two vertices if and only if they
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