الفهرس 
Introduction and Review of LiteratureOnly 14 pages are availabe for public view
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Abstract
Graphs serve as mathematical models to analyze many concrete real-world problems successfully.
Certain problems in physics, chemistry, communication science, computer technology, genetics,
psychology, sociology, and linguistics can be formulated as problems in graph theory. Also, many branches
of mathematics, such as group theory, matrix theory, probability, and topology, have close connections
with graph theory. Some puzzles and several problems of a practical nature have been instrumental in the
development of various topics in graph theory. The famous Königsberg bridge problem has been the
inspiration for the development of Eulerian graph theory. The challenging Hamiltonian graph theory has
been developed from the “Around the World” game of Sir William Hamilton. The theory of acyclic graphs
was developed for solving problems of electrical networks, and the study of “trees” was developed for
enumerating isomers of organic compounds. The well-known four-color problem formed the very basis for
the development of planarity in graph theory and combinatorial topology. Problems of linear programming
and operations research (such as maritime traffic problems) can be tackled by the theory of flows in
networks. Kirkman’s schoolgirl problem and scheduling problems are examples of problems that can be
solved by graph colorings. Many more such problems can be added to this list. This thesis gives some new
results on mutually orthogonal graph squares. These generalize mutually orthogonal Latin squares in an
interesting way. As such, the topic is quite nice and should have broad appeal. In chapter 2 and chapter 3,
we investigate the orthogonal double covers of the complete bipartite graphs and the orthogonal double
covers of the circulant graphs, respectively. Also, the Cartesian product is a helping tool for constructing
the orthogonal double covers of the circulant graphs by new different graph classes. Chapter 4 introduces
the orthogonal double covers of new graphs called the extended complete and extended complete bipartite
graphs. The most important part in the thesis is chapter 5, in which, we introduce some results concerned
with the mutually orthogonal G-squares (MOGSs) where G is a spanning subgraph of Kn,n. By the
Kronecker product, we got several new results concerned with the MOGSs.