GATE | GATE-CS-2005 | Question 10
Let G be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces in the planar embedding of the graph is
An undirected graph is called a planar graph if it can be drawn on a paper without having two edges cross and such a drawing is called Planar Embedding. We say that a graph can be embedded in the plane, if it planar. A planar graph divides the plane into regions (bounded by the edges), called faces. Graph K4 is palanar graph, because it has a planar embedding as shown in
Euler’s Formula : For any polyhedron that doesn’t intersect itself (Connected Planar Graph),the
• Number of Faces(F)
• plus the Number of Vertices (corner points) (V)
• minus the Number of Edges(E)
, always equals 2. This can be written: F + V − E = 2.
Here as given, F=?,V=13 and E=19
So Answer is (B).
This solution is contributed by Nirmal Bharadwaj