A graph is a finite set of dots and connecting links. The dots are called vertices (a single dot is a vertex), and the links are called edges. Each edge must connect two different vertices. A path is a connected sequence of edges showing a route on the graph that starts at a vertex and ends at a vertex. A circuit is a path that starts and ends at the same vertex. An Euler circuits exists if it is possible to travel over every edge of a graph exactly once and return to the starting vertex.
In our applet below you need to find a Euler circuit. To select an edge click a vertex and drag the line to an adjacent vertex. Then continue in this way (starting with the last vertex, until you have traveled all the edges and have arrived back at the starting vertex. The Reset button will return the graph to its original state. The New Graph button will load a new graph.