ABSTRACT
The Swiss mathematician Euler is acknowledged as the father of the theory of graphs, and some of the popular puzzles to which the early theory was applied, for instance the problem of the Königsberg bridges, with which Euler introduced his first paper, are perhaps not too remote from matters of architecture, or at least town planning. Graphs have been used in the theory of electrical networks, to denote the structure of human organizations or social groups, and even in the scientific study of decision-making where vertices signify the decisions to be made and the edges determine the necessary relationship which one decision bears to another. Graphs that it is possible to draw without the edges intersecting are called planar. In Euler’s diagram the graph is in effect a simplified map, and in general it is possible to represent any kind of route map as a graph, where the edges are roads and the vertices junctions.
