Two graphs A and B are shown below: Which one of the following statements is true?
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.
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.
answer : Both A and B are planar