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The total number of planar graphs can be formed with 5 vertices are _____

3 Answers

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1) 5 isolated vertex

2) 2 vertex complete graph and 3 isolated vertex

3) 3 vertex 2 edge and 2 isolated vertex

4) 3 vertex complete graph and 2 isolated vertex

5) 4 vertex chain and one isolated component

6) 4 vertex circuit and one isolated component

7) 4 vertex 5 edge and one isolated component

8) 4 vertex complete graph and one isolated component

9) 5 vertex chain

10) pentagon

11) 5 vertex 6 edge

12) 5 vertex 7 edge

13) 5 vertex 8 edge

14) 5 vertex 9 edge
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The maximum number of graphs possible for graph with 5 vertices are 2n(n-1)/2   =1024.

where only K5 is not planar graph, so total number of planar graph with 5 vertices are 1024-1= 1023.

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