Planar Graphs and Euler’s Formula (VCE SSCE General Mathematics): Quizzes

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Planar Graphs and Euler's Formula
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What is a planar graph?

Graph with no edges crossing except at vertices

Where do edges intersect in a properly drawn planar graph?

Only at vertices

What are two graphs with same vertex connections but different drawings called?

Equivalent or isomorphic graphs

Can all graphs be redrawn in planar form?

No, some are inherently non-planar

What is a face in a planar graph?

A region of space created by the graph

What common mistake do students make when counting faces?

Forgetting to count the infinite face

What is Euler's formula for connected planar graphs?

v+f=e+2v + f = e + 2

What type of graphs does Euler's formula work for?

Any connected planar graph

A planar graph has 4 vertices and 6 faces. How many edges does it have?

88

A planar graph has 4 vertices and 5 edges. How many faces does it have?

33

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