Graphs: Traversing Roads

Abstract

The idea of a graph (or linear graph) is introduced. We start by modelling roads and look at the problem of traversing all roads in an area. The Königsberg bridge problem asks whether this can be done without repeating roads; alternatively, one can try to minimize the number of repeats. The components of graphs (vertices, edges) are defined, and some basic ideas (adjacency, multiple edges, simplicity, connectedness) are discussed.