COT 3100: Applications of Discrete Structures
April 21, 2010
Solution to Homework 8
Lecturer: Prof. My T. Thai
TA: Thang N. Dinh
1
Section 9.1
Problem 10
Solution:
The graph in Exercise 3 is simple. The multigraph in Exercise 4 can be made simple by
removing one of the edges between
a
and
b
, and two of the edges between
b
and
d
. The pseudograph
in Exercise 5 can be made simple by removing the three loops and one edge in each of the three
pairs of parallel edges. The multigraph in Exercise 6 can be made simple by removing one of the
edges between
a
and
c
, and one of the edges between
b
and
d
. The other three are not undirected
graphs. (Of course removing any superset of the answers given here are equally valid answers; in
particular, we could remove all the edges in each case.)
Problem 16
Solution:
Each person is represented by a vertex, with an edge between two vertices if and only
if the people are acquainted.
2
Section 9.2
Problem 6
Solution:
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 Spring '08
 Staff
 Graph Theory, loop, Thang N. Dinh, Multigraph, main inner loops

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