Problem 7

1.

a. Give the vertex set V.

b. Give the Edge set E.

2. Consider the graph with V = [A, B, C, X, Y, Z] and E = [AX, AY, AZ, BB, CX, CY, CZ, YY]. Without drawing a picture of the graph:

a. List all the vertices adjacent to Y.

b. List all the edges adjacent to AY.

c. Find the degree of Y.

d. Find the sum of the degrees of the vertices.

3.

a. Find a path of length 4 from D to E.

b. How many paths are there from D to A, and what are they?

c. Find all circuits of length 2.