الفهرس 
Complete graphsOnly 14 pages are availabe for public view
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Abstract
The subject of this thesis is based on a field of mathematics called graph theory.
In this branch we concentrated on Orthogonal Double Cover (ODC).
The thesis consists of fourth chapters:
Chapter one: Basic Concepts of Graph Theory
It is an introduction 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: The Construction Methods for Orthogonal Double Covers
We construct ODCs of the complete bipartite graphs by using two half
starters and specially by a symmetric starter method. In our work, we use
the construction definition of orthogonal labeling of complete graphs.
Chapter three: ODC of Complete Bipartite Graphs by Disjoint Union of
Graphs
In this chapter, we have proved that there are symmetric starter vectors
on ODC of caterpillar with paths, caterpiller with stars and paths with
cycles. Also, we have proved that there exist a symmetric starter vector of
kite graph with modified kite graph and complete bipartite graphs. The
existence of a symmetric starter vector on ODC of by , where
, ( and ( ), and , where
( and is an even number, are given. Then, we have shown
that the symmetric starter vectors of ODCs for some kinds of different
disjoint union of paths are exist. Finally, the existance on ODC of the
complete bipartite graphs are studied, by some certain disjoint union
of paths. This is done by using a new idea of two half starter vectors, and
show that there exists a half starter vectors of complete bipartite graph,
by disjoint union of graphs.
Some results in this chapter are accepted for publication in ARS Combinatoria Journal,
and some of others accepted for presentation in International Conference for Mathematics
and Applications (ICMA18) and another some accepted for presentation in
International Conference on Mathematics, Statistics & Information Technology (
ICMSIT 2018).
Chapter four: Cyclic Orthogonal Double Cover of Complete Graphs by
Disjoint Union of Graphs
In this chapter, we have shown that there exist CODCs of complete graph
by disjoint union of graphs using orthogonal labelling method.