ABSTRACT
This chapter is concerned with problems of optimization on a network of points connected by weighted edges. The problem is to find a set of edges of minimum cost that does not break communication between any pair of stations in the network. The chapter introduces the basic notions relevant to certain graphs presented. It discusses spanning trees, which are the sparsest possible connected subgraphs of a graph and contains algorithms for the solution of minimal cost network problems. Several other important graph theory problems, including the so-called traveling salesman problem, are discussed. The KnoxOR'Graphs' Mathematica to characterize and display graphs, to make computations, and to implement algorithmic solutions to graph theoretic problems.
