Question

Math Topic: Graphs and Trees (Please show all work if applicable)

G1 = (V1, E1), where V1 = {V,W,X,Y,Z} and E1 = {(V,W),(V,Y),(W,Y),(X,W),(X,X),(Y,Z),(Z,X)}.

For G1 above, please complete the following:
a) Create a computer generated graph, clearly labeling the vertices.
b) Is the graph unconnected, connected, strongly connected, or weakly connected? Why?
c) Does it have a circuit path? If so, give it. If not, say why.
d) List the degrees, in-degrees, and/or out-degrees for each vertex (give in table form).

Answer 1

a. A hand drawn graph of the question is given in the following image.

b.the graph is connected because every pair of vertices are connected by a path without considering the direction. But the graph is weakly connected because there does not exist a directed path from vertex W to V.

c. Here there exist a circuit in the graph given by WYZXW.

d. The indegree and out degree of each vertex is given in the following table.