Graphs (Edexcel A-Level Further Mathematics): Flashcards

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Graph Theory
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Complete graph

Graph where every pair of vertices is connected by a unique edge

Notation: complete graph with nn vertices

KnK_n

Formula: edges in KnK_n

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

Degree of each vertex in KnK_n

n1n-1

Planar graph

Can be drawn on plane without edges crossing

Euler's formula for planar graphs

ve+f=2v - e + f = 2

Non-planar graphs (examples)

K5K_5 and K3,3K_{3,3}

Isomorphic graphs (conditions)

Same # of vertices, edges, and degree sequence

Isomorphic graphs (structural meaning)

Structurally identical, may look different

Edges in K4K_4

6

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