Representation of graphs in diagrams of graph theory

Abstract

The treatise of Dénes König Theorie der endlichen und unendlichen Graphen (1936) includes many diagrams. The style of the diagrams is typical of present-day texts of graph theory. In this treatise, many mathematical recreation problems are treated. Some of the problems were already treated by precedent mathematicians. In some of these early works, the diagrams were given, but the styles were not the same as that of Konig. Moreover, the way to use the diagrams in the early works is different from that of Konig. Examining the diagrams, we will find that a certain type of diagrams became gradually influential. This historical aspect may be related to the formation of concepts of graph, but it will not be discussed here. We will argue that Tarry's talk "Géométrie de situation: Nombre de manières distinctes de parcourir en une seule course toutes les allées d'un labyrinthe rentrant, en ne passant qu'une seule fois par chacune des allées" (1886) played an important role in the way to use the diagrams.