NIELIT 2016 DEC Scientist B (CS) - Section B: 5

Question

Let $G$ be a simple undirected planar graph on $10$ vertices with $15$ edges. If $G$ is a connected graph, then the number of bounded faces in any embedding of $G$ on the plane is equal to:

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

"G is a connected graph", "on the plane" => so the graph is planar and connected

Theorem 1 (Euler's Formula)    Let G be a connected planar graph, and let n, m and f  denote, respectively, the numbers of vertices, edges, and faces in a plane drawing of G. Then n - m + f = 2.

10 - 15 + f =2 => f =7

One of the face is non bounded so, answer is 6.

Ref: http://www.personal.kent.edu/~rmuhamma/GraphTheory/MyGraphTheory/planarity.htm

Comments

Thanks for sharing this, out of all faces 1 face is unbounded