AQA D1 2006 January — Question 3

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2006
SessionJanuary
TopicMinimum Spanning Trees

3
    1. State the number of edges in a minimum spanning tree of a network with 10 vertices.
    2. State the number of edges in a minimum spanning tree of a network with \(n\) vertices.
  1. The following network has 10 vertices: \(A , B , \ldots , J\). The numbers on each edge represent the distances, in miles, between pairs of vertices.
    \includegraphics[max width=\textwidth, alt={}, center]{4a186c87-5f84-4ec3-8cc3-a0ed8721b040-03_1294_1118_785_445}
    1. Use Kruskal's algorithm to find the minimum spanning tree for the network.
    2. State the length of your spanning tree.
    3. Draw your spanning tree.