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The proposition of this thesis is that graph theory should be more widely used by the managers of the U.S. Army. It is a powerful and flexible tool which has been and is being thoroughly researched at the abstract level. Many useful theorems dealing with graphs exist. They need to be put to use. The hypothesis of this paper is that if graph theory is compared to the methods currently being used by the U.S. Army in solving several managerial problems, it will become apparent that graph theory is superior. Numerous authoritative texts about graph theory provide background and historical information for this thesis. However, the primary sources for new concepts of utilization are the recent journals and papers which have been published not only in the mathematical and research fields, but also in the field of management. Following a brief introduction to graph theory, three typical managerial problems which face the U.S. Army are investigated. They are a scheduling problem, a facility layout problem, and a transportation problem. The three problems are solved using techniques which are typical of those used by U.S. Army staffs. They are then solved using a graph theoretic approach. Finally, comparisons of the two techniques are made for each problem. The finding of the study is that graph theory produces better results on some type problems than the techniques now being used. This study also finds that graph theory could be used as an additional approach to some problems to augment the methods now being used. There are also additional areas which need to be explored, at the working level, in which graph theory could play an important role.
