OCR D1 2005 January — Question 2

Exam BoardOCR
ModuleD1 (Decision Mathematics 1)
Year2005
SessionJanuary
TopicCombinations & Selection

2
  1. A graph has six vertices; two are of order 3 and the rest are of order 4. Calculate the number of arcs in the graph, showing your working.
  2. Is the graph Eulerian, semi-Eulerian or neither? Give a reason to support your answer. A simple graph is one in which any two vertices are directly connected by at most one arc and no vertex is directly connected to itself. A connected graph is one in which every vertex is connected, directly or indirectly, to every other vertex.
  3. Explain why a simple graph with six vertices, two of order 3 and the rest of order 4, must also be a connected graph.