Figure 3.1 shows an undirected and unweighted graph. Answer the following questions about the graph. Show all your working. 6 2 1 3

This has 7 points on the graph, Can i see one with 10 like said in the original question?

5. Prim's: What would be the output of Prim's for the following graph (starting at a). Select a valid MST. 7 2 3 6.

Consider the following graph: a Specify a simple cycle. Use only lower case letters. If the graph has any cycles which are not simple and which have no repeated edges, specify one. If there are none enter none Use only lower case letters.

If we have two different non crossing drawings of the same connected graph, is it possible for the two drawings to have a different number of faces?

A circuit is simple if the graph has no repeated edges. Draw a connected, undirected graph with seven vertices and no simple circuit. How many edges does it have?

• If a planar graph has 11 vertices and four times as many edges as faces, how many faces does it have? Is there a planar graph with 13 vertices that has three times more edges than faces?

Can you give a picture or draw the actual connected graph?

2. Answer the following questions about the graph given below. B E a) Does an Euler circuit exist? Why or why not? b) Find a good eulerization for the graph, using as few duplicated edges as possible. How many edges must be added? c) Use the eulerization you developed in part b) to determine a best circuit for this graph, beginning at vertex A. List this path by listing successive vertices. 1 3. Consider the complete graph given below. 24 14 46 B, 32 51 28 a) Find the length of the sorted-edges tour for this graph. Use wiggly lines to indicate this tour. b) Find the length of the nearest-neighbor tour starting at vertex A. Use wiggly lines to indicate this tour.