Draw an undirected graph, if possible (if not possible explain why not that has a. Five vertices and three edges and is connected. b. Five vertices, three edges, and two connected components. c. Five vertices, two edges, and three connected components.

For each graph below determine the minimum number of colors necessary to colorits vertices. Justify your answer, by (i) giving a coloring and (ii) explaining why it is not possibleto use fewer colors. You can represent colors by letters a, b, c, .... To show the coloring, mark eachvertex with its color

Find back-edges for the following graphs starting from smallest nodes, and then find articulation vertices. (A (H) (E) (F B D A E F Please show your work step by step.

One can model a maze by having a vertex for a starting point, a finishing point, dead ends, and all the points in the maze where more than one path can be taken, and then connecting the vertices according to the paths in the maze. a. Construct such a graph for the following maze. 鷗 b. Which traversal DFS or BFS- would you use if you found yourself in a maze and why?