1. Jan 2007

2. AB = 5.5
BC = 8
AI = 9
BD = 13
DE = 9
DG = 11
DF = 12*
HI = 16.5
Total = 84
There should be n – 1 edges
9 – 1 = 8 edges
*EF or GF could also be used

3. Note there are two other spanning trees you could have drawn had you used either EF or GF instead of DF.
You MUST label each vertex with its corresponding letter
There are two other spanning trees you could have drawn had you used either EF or GF instead of DF

4. GH = 5 GE = 7 HJ = 8 EB = 10 BD = 11 HI = 14 DC = 15 AC = 6 FJ = 19
Jan 2009
GH = 5
GE = 7
HJ = 8
EB = 10
BD = 11
HI = 14
DC = 15
AC = 6
FJ = 19
HK = 22
Total = 117
Total length =
117 miles
Next Slide

5. Label and highlight each vertex
Minimum Spanning Tree K I G H J F C A D B E
Label and highlight each vertex

6. AC = 13 AE = 14 EI = 15 CD = 16 CH = 20 EF = 21 FB = 19 BG = 19
Jan 2010
AC = 13
AE = 14
EI = 15
CD = 16
CH = 20
EF = 21
FB = 19
BG = 19
Total Spanning tree = 137

7. G B C A F H E D I

8. ODD vertices at B, C, D, E
BC + DE
BC (22) +
DE (18) = 40
BD + CE
BD (38) +
CE (27) = 65
BE + CD
BE (22) +
CD (16) = 38
Repeat BE + CD = 38
Total route is 307m + (BE + CD) 38 =
345 metres

9. Jan 2011

10. EB = 5
EH = 7
AB = 8
HI = 9
AD = 10
DG = 4
EF = 12
FC = 6
Length of spanning tree = = 61

11. Original Spanning tree = 61
aiii) b) A 8 B A H F B E C I D G C 5 E D F 11 G H I
Original Spanning tree = 61
AB and BE dropped = -13
GE added= 11
New Spanning tree = (61 – ) = 59

12. June 2012

13. AD AB
AC 16
DE 19
EG 10
GI 12
IH 13
IF 17
Total 97
Total 97

14. IF

15. AC

16. Jan 2013
𝐴𝐵=6.1
𝐶𝐵=7.4
𝐵𝐸=9.7
D𝐸=7.2
𝐹𝐸=10.6
𝐸𝐻=12.5
𝐻𝐼=6.7
𝐺𝐻=8.9
𝑇𝑜𝑡𝑎𝑙=69.1
𝑆𝑒𝑒 𝐴𝑏𝑜𝑣𝑒

17. GH

18. EF

19. AB (The Lowest Value)
EH (The Highest Value,
from the Spanning Tree)

20. June 2011

21. AC = 10 CH = 9 FH = 8 CE = 10 ED = 11 Could use CD GH = 13 DB = 14 1 82 6 5 4 7 3
CH = 9
FH = 8
CE = 10
ED = 11
Could use CD
GH = 13
DB = 14

22. 75p AC = 10 CH = 9 FH = 8 CE = 10 ED = 11 GH = 13 DB = 14
Total Spanning Tree = 13 14 G B
75p

23. 70p Delete ALL edges connected to H Total Spanning Tree =10 C 10 E 11 9 11 8 F H D 14 13 14
Total Spanning Tree =
70p G B
From the matrix TWO more edges need to be added,
(AF 11 and any one of GC, GA, GD and GF all 14 are the lowest)

24. June 2014

25. 4 1 2 3 7 5 6
70 +
80 +
80 +
85 +
60 +
110 =
485

26. 70 80 80 85
110 60
FI and IS
FI and GH

27. June 2008
𝑛−1= 𝟏𝟎
𝒏−𝟏

28. AB = 18
BC = 13
BD = 15
CF = 16
DG = 17
GK = 12
KJ = 16
KH = 17
KI = 17
IE = 14
Total Length = 155
Total Length = 155

29. G D B H A E K C I F J

30. June2006
AB = 5
BD = 3
DC = 1
DE = 4
DF = 5
FG = 6
GI = 10
GH = 11
HJ = 13
Total = 58
Total = 58