AQA Further Paper 3 Discrete 2023 June — Question 8

Exam BoardAQA
ModuleFurther Paper 3 Discrete (Further Paper 3 Discrete)
Year2023
SessionJune
TopicGraph Theory Fundamentals

8 The graph \(G\) is shown below.
\includegraphics[max width=\textwidth, alt={}, center]{5ff6e3bb-6392-49cf-b64d-23bc595cd92e-12_301_688_351_676} 8
    1. State, with a reason, whether or not \(G\) is simple. 8
  1. (ii) A student states that \(G\) is Eulerian.
    Explain why the student is correct. 8
  2. The graph \(H\) has 8 vertices with degrees 2, 2, 4, 4, 4, 4, 4 and 4 Comment on whether \(H\) is isomorphic to \(G\)
    8
  3. The formula \(v - e + f = 2\), where
    \(v =\) number of vertices
    \(e =\) number of edges
    \(f =\) number of faces
    can be used with graphs which satisfy certain conditions. Prove that \(G\) does not satisfy the conditions for the above formula to apply.