On Orthogonal Double Covers of Complete Bipartite Graphs by an Infinite Certain Graph-Path and Graph-Cycle
R. A. El-Shanawany *
Department of Physics and Engineering mathematics, Faculty of Electronic Engineering - Menofia University, Menof, Egypt.
*Author to whom correspondence should be addressed.
Abstract
Let F be a certain graph, the graph F-Path denoted by 
d+1(F) path of length d with d + 1 ver-tices (i.e. Every edge of this path is one-to-one corresponding to an isomorphic to the graph F). In the same manner, we define the graph F-Cycle as 
d(F) cycle on d vertices. In this paper, we construct orthogonal double covers (ODCs) of complete bipartite graph Kn,n by d+1(F) and d(F).
Keywords: Graph decomposition, Orthogonal double cover, Symmetric starter