| Exam Board | OCR MEI |
|---|---|
| Module | D1 (Decision Mathematics 1) |
| Year | 2009 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Graph Theory Fundamentals |
| Type | Physical space modeling |
| Difficulty | Moderate -0.8 This question tests basic graph theory concepts through spatial visualization of a die. Part (i) is trivial arithmetic (7-n), part (ii) requires systematic enumeration of adjacent faces on a cube (routine but careful work), and part (iii) requires recognizing a simple polyhedron from its adjacency graph. While it requires spatial reasoning, the concepts are introductory and the execution is methodical rather than requiring problem-solving insight. |
| Spec | 7.02a Graphs: vertices (nodes) and arcs (edges)7.02j Isomorphism: of graphs, degree sequences |
1 The numbers on opposite faces of the die shown (a standard die) add up to 7. The adjacency graph for the die is a graph which has vertices representing faces. In the adjacency graph two vertices are joined with an arc if they share an edge of the die. For example, vertices 2 and 6 are joined by an arc because they share an edge of the die.\\
\includegraphics[max width=\textwidth, alt={}, center]{dab87ac5-eda4-433f-b07a-0a609aca2f65-2_246_213_488_1608}\\
(i) List the pairs of numbers which are opposite each other.\\
(ii) Draw the adjacency graph.\\
(iii) Identify and sketch a solid which has the following adjacency graph.\\
\includegraphics[max width=\textwidth, alt={}, center]{dab87ac5-eda4-433f-b07a-0a609aca2f65-2_287_307_1027_879}
\hfill \mbox{\textit{OCR MEI D1 2009 Q1 [8]}}