Planarity MCQ Quiz in தமிழ் - Objective Question with Answer for Planarity - இலவச PDF ஐப் பதிவிறக்கவும்
Last updated on Mar 20, 2025
Latest Planarity MCQ Objective Questions
Top Planarity MCQ Objective Questions
Planarity Question 1:
The chromatic number of a planar graph is not greater than __________
Answer (Detailed Solution Below)
Planarity Question 1 Detailed Solution
The chromatic number of a planar graph is no greater than 4. (The Four Colour Theorem)
Planarity Question 2:
A Graph G is a connected planar simple graph with ‘e’ edges and ‘v’ vertices, with v > 3 , if all cycles in G have length > 4 then which of the following relations always hold?
Answer (Detailed Solution Below)
Planarity Question 2 Detailed Solution
The sum of the degrees of the regions is equal to twice the number of edges. But each region must degree > 4 because all cycles have length > 4. So we have 2e > 4 r
By Euler’s formula: v – e + r = 2, so combining these
e – v + 2 < e ⇒ e < 2v – 4
Planarity Question 3:
Maximum number of edges in a triangle free, simple planar graph of 10 vertices is:
Answer (Detailed Solution Below) 16
Planarity Question 3 Detailed Solution
Planarity Question 4:
Graph G (V, E) is connected planar with no cycles of length less than 4,
if |V| = 15 then maximum value of |E| is:Answer (Detailed Solution Below) 26
Planarity Question 4 Detailed Solution
For connected planar graphs with no cycles of length 3.
|E| ≤ 2 |V| - 4
otherwise
|E| ≤ 3 |V| - 6
for all connected planar graphs.