Jan 2007

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

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

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

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

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

G B C A F H E D I

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

Jan 2011

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

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 – 13 + 11) = 59

June 2012

AD 4 AB 6 AC 16 DE 19 EG 10 GI 12 IH 13 IF 17 Total 97 Total 97

IF

AC

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

GH

EF

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

June 2011

AC = 10 CH = 9 FH = 8 CE = 10 ED = 11 Could use CD GH = 13 DB = 14 1 8 2 6 5 4 7 3 CH = 9 FH = 8 CE = 10 ED = 11 Could use CD GH = 13 DB = 14

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

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)

June 2014

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

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

June 2008 𝑛−1= 𝟏𝟎 𝒏−𝟏

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

G D B H A E K C I F J

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