AQA D1 2008 January — Question 3

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2008
SessionJanuary
TopicMinimum Spanning Trees

3 The diagram shows 10 bus stops, \(A , B , C , \ldots , J\), in Geneva. The number on each edge represents the distance, in kilometres, between adjacent bus stops.
\includegraphics[max width=\textwidth, alt={}, center]{92175666-ef7a-4dca-9cdb-ebde1b40b2c9-03_595_1362_422_331} The city council is to connect these bus stops to a computer system which will display waiting times for buses at each of the 10 stops. Cabling is to be laid between some of the bus stops.
  1. Use Kruskal's algorithm, showing the order in which you select the edges, to find a minimum spanning tree for the 10 bus stops.
  2. State the minimum length of cabling needed.
  3. Draw your minimum spanning tree.
  4. If Prim's algorithm, starting from \(A\), had been used to find the minimum spanning tree, state which edge would have been the final edge to complete the minimum spanning tree.