Chapter 10
24. A
is given the label
(,0).
Next
C
is labelled
(A, 2),
then
D
is labelled
(A,
4) and
B
is
(A,
5). Then G is
labelled
(D,
6) and
F
is
(C,
7) Then
E
is labelled
(G,8)
and
H
is
(F,9)
or
(G,
9). Finally,
I
is labelled
(F,
11). These labels give the required lengths. One
shortest path from
A
to
H
is
AC F H; ADG H
is
another, since
H
could also have been labelled
(G,
9).
25. First,
A
is given the label 0 and all other vertices are
given temporary labels of
00. Next,
B, C, D
and
E
are given temporary labels of 5,2,4 and 10,
respectively, and 2 becomes the permanent label on
C.
Now the temporary label on
E
is decreased to 9
while
F
is given a temporary label of 7. So
D
gets the
next permanent label, 4. Now G acquires a temporary
label of 6
(E's
temporary label of 9 does not change)
and
B
gets the next permanent label, 5. No new
temporary labels are assigned, so the next permanent
label is 6 on G. Now
E's
temporary label is decreased
to 8, while
H
gets a temporary label of 9.
291
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 Summer '10
 any
 Graph Theory, Shortest path problem, permanent label, temporary label

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