(a) 10 5 (b) 10 3 (11 7

Show a simple disconnected graph with 6 vertices and 2 connected components.

Find the number of connected components for the following graph.

If there is an Euler path that starts at AA and ends at some other vertex, give it. Otherwise enter DNE.This should be a list of letters, from A to the other vertex: e.g. ACBDEAD (if that were even possible!). Path:  Since this is a planar graph, the number of regions - arcs + nodes equals what number?

V4 Draw the complement of the graph:

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

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.

18. Show that in a simple graph with at least two vertices there must be two vertices that have the same degree.

Give an example of a graph that has all of the following properties. (Give a single graph as the answer.) (i) It does not have any articulation point. (ii) It does not have a Hamiltonian cycle (iii) It does not have a valid vertex coloring with only 2 colors.

• 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?