GATE CSE 1992 | Question: 01,x

Question

Maximum number of edges in a planar graph with $n$ vertices is _____

Answer 1

Answer: 3n - 6

Ref: http://mathoverflow.net/questions/124116/maximum-number-of-edges-in-a-planar-graph

Comments

i think it is 2n-2

if n=2 then edges will be 1 it is also a planar graph but according to your equation it becomes 0

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@ suneetha 2n-4 (not 2n-2) its true when the graph has no cycle of lenght 3.

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they didn't represent about whether it should have cycle or not?

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if n is even then the equation comes like 2(n-1)
if n is odd then the equation comes like 2n-1
then what is the answer for this question?