Undirected graphs and networks

WorkSHEET 21.2
178 General Mathematics
11 For the network shown in the diagram at right, find the
shortest distance between:
a A and H b E and G.
12 A tour of six country towns is to start and finish at
Bendigo. Find the shortest distance tour.
13 The distance, in km, between five towns is shown in the table below.
B C D E
A 300 353 417 280
B 219 453 345
C 291 402
D 258
Note: The shaded region indicates that there is no road connecting the two towns.
a Transfer the information from the above table onto a copy of the A
graph at right.
B
b A tour is planned to start and finish at A and visit all of the towns. E
c
Find the shortest distance for the tour.
If the tour were to start and finish at C, would the shortest distance
be the same?
D
C
d A new tour, starting and finishing at A, is planned to visit all the towns and a
further town, F. The distances from B to F, C to F and E to F are 476, 429 and
319 km respectively. Find the shortest distance tour now possible.
14 multiple ultiple choice
A Hamiltonian circuit for the graph at right is:
A A–D–E–C–F–G–A B A–D–B–C–E–C–F–G–A
C A–D–E–C–B–F–G D A–D–E–C–B–F–G–A
E A–G–F–B–D–C–E–A
15 multiple ultiple choice
The length of the shortest Hamiltonian circuit is:
A 53 km B 47 km C 56 km
D 40 km E 51 km
10
A
E
14
6 10
C
13
13
11
12
22
B
8
G
5
9 H
9 4 D
F
Mildura
225 km
103 km
Ouyen 140 km
Swan Hill
60 km
212 km
Kerang
115 km
Horsham
219 km Bendigo
13 km
E
G
247 km
234 km
A D
B
F C
2 km
D
15 km
A 3 km B
5 km
17 km
F
9 km
12 km
14 km
E
12 km
C