Graphs and Networks 2 (AQA A-Level Further Maths): Quizzes

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Planar Graphs and Isomorphisms
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How is an undirected loop at a vertex recorded in an adjacency matrix?

As 2

What property does an adjacency matrix have for an undirected graph?

It is symmetric

How do you find the adjacency matrix of GG' from the matrix of GG?

Swap 0s and 1s, keep diagonal unchanged

What graph results from combining a simple graph GG with its complement GG'?

The complete graph KnK_n

How many edges does the complete graph KnK_n have?

n(n1)2\frac{n(n-1)}{2}

If two graphs have the same degree sequence, are they definitely isomorphic?

No, it's necessary but not sufficient

For a planar graph with V=7V=7, E=10E=10, how many faces FF are there using Euler's formula?

5

A graph has V=6V=6 and E=16E=16. What does E3V6E \leq 3V - 6 tell us?

Graph is definitely non-planar

Which complete graphs are non-planar?

KnK_n if n5n \geq 5

According to Kuratowski's theorem, when is a graph non-planar?

If it has subdivision of K5K_5 or K3,3K_{3,3}

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