الفهرس 
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Abstract
The subject of this thesis is based on a eld of mathematics called graph theory. In this
branch we concentrated on Orthogonal Double Cover (ODC). Which initiated the study of
orthogonal double covered and surveying the current state of methods and results on ODCs and
common generalizations. In addition we present a number of new examples and results. The
thesis consists of four chapters:
Chapter one: Review of Literature and, Basic Concepts of Graph Theory. It is an introduc-
tion for the following chapters and contains some of the main concepts of graph theory which
will be used through out our work. Also it is illustrates complete bipartite graphs, complete
graphs and orthogonal double cover (ODC) of each graph.
Chapter two: Construction mutually orthogonal graph squares (MOGS) using starter func-
tions which represent two disjiont unions of certain trees graph squares (2DUCTGS):
Chapter three: Construction mutually orthogonal graph squares (MOGS) using starter
functions which represent three disjoint unions of certain trees graph squares (3DUCTGS):
Chapter four: Conclusion and recommendations for future research.
Finally, the four chapters are followed by a general conclusion extracted from the thesis.