AQA
Further AS Paper 2 Discrete
2020
June
— Question 4
Exam Board
AQA
Module
Further AS Paper 2 Discrete (Further AS Paper 2 Discrete)
Year
2020
Session
June
Topic
Graph Theory Fundamentals
4 The connected planar graph \(P\) is Eulerian and has at least one vertex of degree \(x\).
Some of the properties of \(P\) are shown in the table below.
Number of
vertices
Number of
edges
Number of
faces
\(3 x + 6\)
\(x ^ { 2 } + 8 x\)
\(2 x ^ { 2 } + 2\)
Deduce the value of \(x\).
Fully justify your answer.
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