# UGCNET-Dec2012-III: 46

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Two graphs A and B are shown below: Which one of the following statements is true? 1. Both A and B are planar
2. Neither A nor B is planar
3. A is planar and B is not
4. B is planar and A is not

recategorized
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Ma'am you missed out the Graphs

Planar Graph:-A graph G is planar if it can be drawn in the plane in such a way that no two edges meet each other except at a vertex to which they are incident.

Here Both S1 and S2 are Planar graph .Here no edges cross each other. Hence,Option(A)Both A and B Planar.

selected

Constructing planar version of given graph is quite time consuming. We can solve such questions quickly using the relation :

If E is the number of edges and V is the number of vertices, and  E<= 3(V-2),  graph is  planar, otherwise it is Not Planar.

1. A) V=4; E=6; 3*(V-2)=3(4-2)=6=E  //Planar
2. B) V=8; E=12 3*(V-2)=3(8-2)=18               E=12<18   //Planar

answer : Both A and B are planar

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But this solution is not applicable on Peterson graph which is not planar
0
Thanks

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