OCR MEI D1 2010 June — Question 3

Exam BoardOCR MEI
ModuleD1 (Decision Mathematics 1)
Year2010
SessionJune
TopicGraph Theory Fundamentals

3 Traffic flows in and out of a junction of three roads as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{839adc96-1bea-44ef-917e-f03e396a3061-3_296_337_333_863} Assuming that no traffic leaves the junction by the same road as it entered, then the digraph shows traffic flows across the junction.
\includegraphics[max width=\textwidth, alt={}, center]{839adc96-1bea-44ef-917e-f03e396a3061-3_362_511_852_776}
  1. Redraw the digraph to show that it is planar.
  2. Draw a digraph to show the traffic flow across the junction of 4 roads, assuming that no traffic leaves the junction by the same road as it entered.
    \includegraphics[max width=\textwidth, alt={}, center]{839adc96-1bea-44ef-917e-f03e396a3061-3_366_366_1512_854}
    (Note that the resulting digraph is also planar, but you are not required to show this.)
  3. The digraphs showing flows across the junctions omit an important aspect in their modelling of the road junctions. What is it that they omit?