OCR MEI D1 2010 June — Question 3 8 marks

Exam BoardOCR MEI
ModuleD1 (Decision Mathematics 1)
Year2010
SessionJune
Marks8
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TopicGraph Theory Fundamentals
TypeNetwork and route modeling
DifficultyModerate -0.8 This is a straightforward graph theory question requiring basic understanding of planar graphs and digraph representation. Part (i) is a simple redrawing exercise, part (ii) extends the pattern mechanically from 3 to 4 roads, and part (iii) asks for a conceptual observation about real-world modeling. No complex algorithms, proofs, or multi-step problem-solving required—mostly recall and pattern recognition at D1 level.
Spec7.02a Graphs: vertices (nodes) and arcs (edges)7.02k Digraphs: directed graphs, indegree and outdegree7.02l Planar graphs: planarity, subdivision, contraction
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?
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}\\
(i) Redraw the digraph to show that it is planar.\\
(ii) 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.)\\
(iii) The digraphs showing flows across the junctions omit an important aspect in their modelling of the road junctions. What is it that they omit?

\hfill \mbox{\textit{OCR MEI D1 2010 Q3 [8]}}
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