AQA
Further Paper 3 Discrete
2021
June
— Question 6
6 marks
Exam Board
AQA
Module
Further Paper 3 Discrete (Further Paper 3 Discrete)
Year
2021
Session
June
Marks
6
Topic
Graph Theory Fundamentals
6
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
Explain why \(K _ { 6 }\), the complete graph with 6 vertices, is not planar.
Fully justify your answer.