MAT 226 – Homework #2
1. Let 𝐺 = {𝑉, 𝐸} have a drawing as shown below:
2. Let 𝐺 = {𝑉, 𝐸} have a drawing as shown below:
a) What is the vertex set V?
a) What is the vertex set V?
b) What is the edge set E?
b) What is the edge set E?
c) What is the order of G?
d) Is G connected?
e) Is G a simple graph or multigraph?
f) What is the degree of each vertex?
A=
B=
C=
c) What is the size of G?
d) Is G connected?
e) Is G a simple graph or multi graph?
f) What is the degree of each vertex?
A=
B=
C=
D=
E=
F=
D=
E=
g) Are B and E adjacent?
g) Are B and D adjacent?
h) Are A and C adjacent?
h) Are A and D adjacent?
F=
2. If 9 people shake hands with each other, how many handshakes took place? Please show all work for full
credit.
3. Given these two graphs, determine a) if they are equal; and b) if they aren’t equal, then are they isomorphic.
G1 : V1 = {a, b, c, d , e} E1 = {{a, b},{a, c},{a, e},{b, d},{b, e},{c, d}}
4. Which of the following graphs are bipartite? If they are, write out the two sets A and B that are bipartite. If
they are not, explain why.