MATH Section 10.2

Consider the directed multigraph. Click and drag the vertices (in the right column) to their number of in-degrees (in the left column).

1 in-degree: d 2 in-degrees: a c 3 in-degrees: b

Consider the directed multigraph. Click and drag the vertices (in the right column) to their number of out-degree (in the left column).

1 out-degree: c d 2 out-degrees: a 4 out-degrees: b

Consider an acquaintanceship graph, where vertices represent all the people in the world. Click and drag the phrases on the right to match with the phrases on the left.

The degree of a vertex v is the number of people v knows The neighborhood of a vertex v is the set of all people whom v knows. An isolated vertex is a person who knows no one. A pendant vertex is a person who knows just one other person. If the average degree is 1000, then the average person knows 1000 other people.

Consider the directed graph shown in the figure. What is the number of edges in the given graph? Find the relation between the number of edges, and the in-degree and out-degree.

The number of edges is 13. The number of edges, the sum of the in-degrees, and the sum of the out-degrees are all equal.

Consider a graph having degree sequence 4, 3, 3, 2, 2. The graph for which the degree sequence is 4, 3, 3, 2, 2 is

True

Consider the given bipartite graphs. For what values of n is Cn bipartite?

for all even n ≥ 4

Consider the given bipartite graphs. For what value of n is Kn bipartite?

for n = 2

Consider the directed multigraph. How many edges are there for the given graph?

8

Consider the directed graph shown in the figure. Determine the sum of the in-degrees of the vertices for the given graph.

13

Consider the directed graph shown in the figure. Determine the sum of the out-degrees of the vertices for the given graph.

13

Consider the directed multigraph. What is the number of vertices for the given graph?

4

Consider a graph having degree sequence 4, 3, 3, 2, 2. How many edges does a graph have if its degree sequence is 4, 3, 3, 2, 2? (You must provide an answer before moving to the next part.)

7