The aim of the lecture is to show that Graphs Theory is a useful tool for description and analysis of multivarious problems benefit from effortless illustration and being a useful starting point for efficient algorithms. An emphasis is put on algorithms, how to evaluate their efficiency, and efficient data manipulation.
One of the most exciting developments in Operations Research in recent years has been the unusually rapid advance in both the methodology and application of network optimization models. However, a good introductionary chapter is a short glance in the history of graphs theory beginning with the problem of the seven bridges at Königsberg. A number of algorithmic breakthroughs in the 1970s and 1980s have had a major impact, as have ideas from computer science concerning data structure and efficient data manipulation. Therefore the second chapter delves into issues of data structures, etc, that are so vital to successful large-scale implementation or in other words that are so vital to solve huge problems. The next chapters deals with four problem types - minimum spanning tree, shortest path problem, maximum flow problem, and combinatorial optimization problem. The last problem type considered is project planning and control with PERT and CPM.