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

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Planar Graphs and Isomorphisms
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Planar graph definition

Graph drawable in plane without edge crossings

Euler's formula for planar graphs

V+FE=2V + F - E = 2

Complement GG' of graph GG

Same vertices, only edges NOT in GG

Complete graph KnK_n definition

Every pair of vertices connected by an edge

Number of edges in KnK_n

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

Isomorphic graphs meaning

Graphs with the same structure

Adjacency matrix

Matrix showing connections between each vertex pair

Faces in planar graph

Regions bounded by edges, including infinite outer region

Simple planar graph edge inequality

E3V6E \leq 3V - 6

Kuratowski's theorem for non-planarity

Graph has subdivision of K5K_5 or K3,3K_{3,3}

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