Investigate! An Euler path, in a graph or multigraph, is a walk through the graph which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. Our goal is to find a quick way to check whether a graph (or multigraph) has an Euler path or circuit. 1. Which of the graphs below have Euler paths? Which have Euler circuits? SRIXI> 2. List the degrees of each vertex of the graphs above. Is there a connection between degrees and the existence of Euler paths and circuits? 3. Isit possible for a graph with a degree 1 vertex to have an Euler circuit? If so, draw one. If not, explain why not. What about an Euler path? 4. What if every vertex of the graph has degree 2. Is there an Euler path? An Euler circuit? Draw some graphs. 5. Below is part of a graph. Even though you can only see some of the vertices, can you deduce whether the graph will have an Euler path or circuit