On Orthogonal Double Covers of Complete Bipartite Graph by the Disjoint Union of Graphs

Abstract

The existence problem of the orthogonal double covers of the graphs is a well-known problem in the theory of combinatorial designs. In this paper, we construct the orthogonal double covers of the complete bipartite graph by the disjoint union of paths, copies of a caterpillar, copies of a certain path, and by other certain defined graph. We use the vector method as a helping tool for constructing our results, the advantage of this method is that it is accessible to discrete mathematicians not intimately familiar with the theory of the orthogonal double covers.