Hon Discrete 5.1 – 5.3 WORKSHEET NAME: _________________________
#1) For the following graph…
a) What is the degree of each vertex?
A
B
b) Find all bridges.
C
D
E
F
c) Find all circuits.
d) Find the longest path between any 2 vertices.
#2) For the following graph…
A) Find a circuit of …
a. Length 3?
A
B
C
D
b. Length 4?
E
c. Length 5?
F
d. Length 8?
B) Find a path from B to F of length 3 and length 4?
C) Find a path from A to C of length 3 and length 5?
G
#3) For the following graph…
a) What is the degree of each vertex?
A
B
D
b) Is this a connected graph?
C
E
c) Identify any loops or multiple edges.
F
G
For #4 – 10, DRAW A GRAPH THAT MEETS THE GIVEN DESCRIPTION:
 Use the space provided. Hint: Start with the total number of vertices required
#4) Draw a connected graph that has 10 edges and 6 vertices.
#5) Draw a graph that has 5 vertices and has 3 bridges.
#6) Draw a disconnected graph of 3 vertices and has 1 bridge in a component.
#7) Draw a graph that has 3 even degrees and 4 odd vertices. There is no limit on the
number of edges you can use.
#8) Draw a connected graph that has 2 even vertices and 2 odd vertices.
#9) Draw a graph with 2 loops, multiple edges, and one vertex.
#10) Draw a graph with 5 even vertices that is disconnected with 3 components.
Hon Discrete 5.1 – 5.3 WORKSHEET
NAME: _____ANSWER KEY__________
#1) For the following graph…
a) What is the degree of each vertex?
A=2B=3 C=1 F=2 E=3 F=3
A
B
b) Find all bridges.
AC, AB, EF
c) Find all circuits.
B,D,E,B and FF
C
D
E
F
d) Find the longest path between any 2 vertices.
C, A, B, D,E,F, F = Length 6
#2) For the following graph…
A) Find a circuit of …
a. Length 3? A,D,F,A or B,C,E,B
A
B
C
b. Length 4? D,E,G,F,D
c. Length 5? A,D,E,G,F,A
D
E
d. Length 8?A, D, E, B, C, E, G, F, A
B) Find a path from B to F of length 3 and length 4?
3: B, E, D, F or B, E, G, F
4: B, C, E, D, F or B, C, E, G, F or B, E, D, A, F
F
G
C) Find a path from A to C of length 3 and length 5?
3: A, D, E, C
5: A, D, F, G, E, C or A, F, D, E, B, C or A, F, G, E, B, C
#3) For the following graph…
a) What is the degree of each vertex?
A = 3, B = 2, C = 2, D = 4, E = 2, F = 3, G = 4
A
B
C
b) Is this a connected graph?
NO
D
d) Identify any loops or multiple edges.
E
LOOPS: DD
Multiple Edges: EG, AF
F
G
For #4 – 10,CREATE THE FOLLOWING GRAPHS: POSSIBLE SOLUTIONS
 Use the space provided and any extra paper as needed.
4) Draw a connected graph that has 10 edges and 6 vertices.
5) Draw a graph that has 5 vertices and has 3 bridges.
6) Draw a disconnected graph of 3 vertices and has 1 bridge in a component.
7) Draw a graph that has 3 even degrees and 4 odd vertices. There is no limit on the number of edges you
can use.
8) Draw a connected graph that has 2 even vertices and 2 odd vertices.
9) Draw a graph with 2 loops, multiple edges, and one vertex.
10) Draw a graph with 5 even vertices that is disconnected with 3 components.