UC Berkeley, Spring 2009
Solutions to Homework # 11 (due April 27)
§
9.1, #13: See diagrams.
§
9.1, #27: This is best represented by a directed multigraph which allows loops
but not duplicate edges.
§
9.2, #5: No, because
X
v
∈
V
deg
v
= 45 which is odd; but this is impossible by the
Handshaking Theorem.
§
9.2, #20: See diagrams.
§
9.2, #29: a)
K
n
has
n
vertices and
(
n
2
)
edges.
b)
C
n
has
n
vertices and
n
edges.
c)
W
n
has
N
+ 1 vertices and 2
n
edges.
d)
K
m,n
has
m
+
n
vertices and
mn
edges.
e)
Q
n
has 2
n
vertices and
n
2
n

1
edges (since each vertex has degree
n
).
§
9.2, #31: a) 3,3,3,3
b) 2,2,2,2
c) 4,3,3,3,3
d) 3,3,2,2,2
e) 3,3,3,3,3,3,3,3
§
9.2, #36: a) Not graphic; the vertex with degree 5 must be adjacent to each of
the others, but one of these has degree 0.
b) Not graphic; a simple graph with 6 vertices cannot have a vertex of
degree 6.
c) The cycle
C
6
is one such graph.
d) Not graphic: the degrees sum to an odd number, violating the Hand
shaking Theorem.
e) See diagrams.
f) See diagrams.
g) The wheel
W
5
is one such example.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 STRAIN
 Math, Graph Theory, Vertex, vertices

Click to edit the document details