GateAI
Discrete Mathematics

GATE CSE 2011 · Q17

MCQ1 markEasy

Time

K4 and Q3 are graphs with the following structures. Which one of the following statements is TRUE in relation to these graphs?

GATE CSE 2011 Q17 diagram

Select one answerSingle correct

Pick an option to check

Solution

Step-by-step verified solution

Official answer: B) Both K4 and Q3 are planar

Discrete Mathematics

A graph is planar if it can be drawn in a plane without any of its edges crossing.

  1. Graph K4K_4 (complete graph on 4 vertices): It has V=4V = 4 vertices and E=6E = 6 edges. K4K_4 can be drawn in the plane without edge crossings by placing one vertex inside the triangle formed by the other three and connecting it to all three vertices. Hence, K4K_4 is planar.

  2. Graph Q3Q_3 (3-dimensional hypercube / 3-cube graph): It has V=8V = 8 vertices and E=12E = 12 edges. It is isomorphic to the 3D cube graph, which can be drawn as a planar graph (the standard Schlegel diagram of a cube: an inner square inside an outer square with corresponding vertices connected). Since it contains neither K5K_5 nor K3,3K_{3,3} as a minor/subdivision, by Kuratowski's theorem, Q3Q_3 is planar.

Therefore, Both K4K_4 and Q3Q_3 are planar, making (B) the correct choice.

Try the question first, then check your work.

Think the official key or this write-up is wrong?

Report error or challenge

Examiner trap

The misconception this question tests

This Discrete Mathematics previous year question is Q17 of the GATE CSE 2011 paper. Find more GATE CSE PYQs on Discrete Mathematics in Engineering Mathematics, or browse all GATE CSE PYQs.

Free diagnostic

Where do you stand for GATE?

Take the 20-minute diagnostic: the 3 topics that cost you the most marks, and a rank range. Or sit 5 related Discrete Mathematics PYQs now with no account.

One GATE CSE PYQ every morning

An official question by email at 7 AM IST, with a link to its verified solution. Unsubscribe in one click.

Discrete Mathematics in GATE CSE

Discrete Mathematics has 50 GATE CSE PYQs across 23 papers from 2011 to 2026. 18 of them are 1-mark MCQs like this one, and it is the only one in GATE CSE 2011.

How GATE tests Discrete Mathematics

More from GATE CSE 2011

Share this solution

A plain-text card for WhatsApp or Telegram study groups.

GateAI solution cardGATE CSE 2011 · Q17 · MCQ

K4 and Q3 are graphs with the following structures. Which one of the following statements is TRUE in relation to these graphs?

Topic-wise GATE CS PYQs with verified steps

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.