AQA Further Paper 3 Discrete 2021 June — Question 6 6 marks

Exam BoardAQA
ModuleFurther Paper 3 Discrete (Further Paper 3 Discrete)
Year2021
SessionJune
Marks6
TopicGraph Theory Fundamentals

6
  1. A connected planar graph has \(( x + 1 ) ^ { 2 }\) vertices, \(( 25 + 2 x - 2 y )\) edges and \(( y - 1 ) ^ { 2 }\) faces, where \(x > 0\) and \(y > 0\) Find the possible values for the number of vertices, edges and faces for the graph.
    [0pt] [6 marks]
    LL
    6
  2. Explain why \(K _ { 6 }\), the complete graph with 6 vertices, is not planar. Fully justify your answer.