Graph theory

Abstract

Graph theory had its beginning in Euler’s solution of what is known as the Konigsberg Bridge problem. Kirchhoff developed the theory of trees in 1847 as a tool in the study of electrical networks. This was the first application of graph theory to a problem in physical science. Electrical network theorists have since played a major role in the phenomenal advances of graph theory that have taken place. A comprehensive treatment of these developments may be found in Ref. [1]. In this chapter, we develop most of those results which form the foundation of graph theoretic study of electrical networks.