AQA D1 2012 January — Question 2

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2012
SessionJanuary
TopicMatchings and Allocation

2
  1. Draw a bipartite graph representing the following adjacency matrix.
    \cline { 2 - 7 } \multicolumn{1}{c|}{}\(\mathbf { 1 }\)\(\mathbf { 2 }\)\(\mathbf { 3 }\)\(\mathbf { 4 }\)\(\mathbf { 5 }\)\(\mathbf { 6 }\)
    \(\boldsymbol { A }\)110011
    \(\boldsymbol { B }\)010011
    \(\boldsymbol { C }\)100011
    \(\boldsymbol { D }\)011101
    \(\boldsymbol { E }\)000011
    \(\boldsymbol { F }\)000001
  2. Given that \(A , B , C , D , E\) and \(F\) represent six people and that 1, 2, 3, 4, 5 and 6 represent six tasks to which they may be assigned, explain why a complete matching is impossible. \begin{verbatim} QUESTION PART REFERENCE \end{verbatim}