1.2 Finding Euler Circuits - Video

Key Ideas The valence of a vertex is the number of edges which meet at that vertex. This will be either an even or odd positive integer. If the vertex is isolated, then it will have valence zero. A graph is connected if for every pair of vertices there is at least one path connecting these two vertices. A connected graph has no vertices with valence zero. According to Euler’s theorem, a connected graph has an Euler circuit if the valence at each vertex is an even number. If any vertex has an odd valence, there cannot be an Euler circuit. In finding an Euler circuit, never “disconnect” the graph by using an edge that is the only link between two parts of the graph not yet covered.