The following questions are presented as a quiz on Blackboard. You will have only one attempt at completing this quiz. - Let S = {u,v,w,x,y}. How many different graphs are there which have vertex set S? - Identify whether each of the following statements is true or false. - If G is a subgraph of H, then alpha(G) =alpha(H) - If G is a subgraph of H, then omega(G) = omega (H) - Suppose F is a forest with loo vertices and 20 components. How many edges must F have? - Let G be a properly colored graph and let us suppose that one of the colors used is red. The set of all red-colored vertices have a special property. What is it? Solution If G is subgraph of H, then all vertices and edges in G will exist in H. alpha(G)<= alpha(H) is true. alpha(G)>= alpha(H) is false. w(G)<= w(H) is true. w(G)>= w(H) is false..