الفهرس 
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Abstract
Graph theory is one of the very important elds as it has contributed to many elds of mathematics such as medicine, engineering and computer science, and its applications are in indirect ways, internet networks, the way devices are connected through networks, and the methods of connecting citiesc and circuits, are also used to represent molecular bonds between compounds. For example, a map represents a hypothetical map where each city represents a point on the map or a vertex in the map, and each edge connecting two points or two vertices is a way to connect two cities. Typically, a graph is a shape made up of points called vertices and links called edges. Graph theory is used all the time in our daily life because it analyzes big graphs and turns them into small graphs that can be used to solve problems easily. An important branch of graph analysis is the Orthogonal Double Covers (ODC). This thesis contributes to the study of the orthogonal double covers of the complete bipartite graph by a disjoint union of the certain cyclic graph and also contributes to the study of the orthogonal double covers of the complete bipartite graph by using general cases.