An application of graph theory to algebra

Abstract

2. Graph theory.Definition 1.An oriented graph T consists of a set of points (called vertices) and a set of oriented segments (called edges) joining certain of these vertices.Examples of parts of graphs are shown in Figures 1 to 10 below.Note that we allow a vertex to be joined to itself and we also allow two vertices to be joined in many ways.Let V be the number of vertices of the graph and E the number of edges.I will only be concerned here with the case in which E and V are finite.If P is any vertex of T, the order of P is defined to be the total number of edges beginning or ending at P. An edge which joins P to itself is to be counted twice.The flux of P is defined to be the num-

Locations

• Proceedings of the American Mathematical Society - View - PDF