326
Solutions to Exercises
but it also must be cheaper than any other selection of edges connecting the six other towns to
A.
This is in fact the case, because
ADEFCBG
consists of the six edges of smallest weight in the
entire graph!
A
10. (a) The minimum cycle is
ACBDA
(or
ADBCA,
in reverse) with a
total of90.
C
D
c
c
DB
c
B
A
A A
AA A
(b) The minimum path is
ADCBEA
which, in reverse, is the same as
AEBCDA,
with a total of
220.
A
AAAAAAAAAAAAAAAAAAAAAAAA
11. (a) Give the tree
n
vertices. Then there are
n

1 edges, so the sum of the degrees is
2(n
1). This
gives
1
1
100
+
20(6)
+
 120)4
+
 120)2
=

1)
=
2n

2
so
n
=
138. The number of vertices of degree 2 is
~
(n
 120)
=
9.
(b) Let there be
k
vertices of degree 1 and
n
in all. Since the sum of the degrees is 21 £ 1
This is the end of the preview.
Sign up
to
access the rest of the document.
 Summer '10
 any
 Graph Theory, Vertex, Binary relation, vertices

Click to edit the document details