need quick solution

4. An Euler path in a graph or multigraph is a path which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. Your goal is to find a quick way to check whether a graph (or multigraph) has an Euler path or circuit. (a) Which of the graphs/multigraphs below have Euler paths? Which have Euler circuits? (6) List the degrees of each vertex on the graphs above. Notice anything? Write your observations. (c) Is it possible for a graph with a degree 1 vertex to have an Euler path or circuit? What if all the vertices have degree 27 Draw some graphs and make a conjecture. (d) What is the smallest number of bridges you must add to the Knigsberg graph (shown below) to get an Euler path? What about an Euler circuit? (e) 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? (f) Edward A. Mouse has just finished his brand new house. The floor plan is shown below: Edward wants to give a tour of his new pad to a lady-mouse-friend. Is it possible for them to walk through every doorway exactly once? If so, in which rooms must they begin and end the tour? Explain by creating a graph and using graph theory terms. 4. An Euler path in a graph or multigraph is a path which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. Your goal is to find a quick way to check whether a graph (or multigraph) has an Euler path or circuit. (a) Which of the graphs/multigraphs below have Euler paths? Which have Euler circuits? (6) List the degrees of each vertex on the graphs above. Notice anything? Write your observations. (c) Is it possible for a graph with a degree 1 vertex to have an Euler path or circuit? What if all the vertices have degree 27 Draw some graphs and make a conjecture. (d) What is the smallest number of bridges you must add to the Knigsberg graph (shown below) to get an Euler path? What about an Euler circuit? (e) 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? (f) Edward A. Mouse has just finished his brand new house. The floor plan is shown below: Edward wants to give a tour of his new pad to a lady-mouse-friend. Is it possible for them to walk through every doorway exactly once? If so, in which rooms must they begin and end the tour? Explain by creating a graph and using graph theory terms