K4 and Q3 are graphs with the following structures. Which one of the following statements is TRUE in relation to these graphs? A) K4 is planar while Q3 is not B) Both K4 and Q3 are planar C) Q3 is planar while K3 is not D) Neither K4 nor Q3 is planar

Official answer: B) Both K4 and Q3 are planar. Explanation: A graph is planar if it can be drawn in a plane without any of its edges crossing. 1. Graph K4 (complete graph on 4 vertices): It has V = 4 vertices and E = 6 edges. K4 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, K4 is planar. 2. Graph Q3 (3-dimensional hypercube / 3-cube graph): It has V = 8 vertices and E = 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 K5 nor K3,3 as a minor/subdivision, by Kuratowski's theorem, Q3 is planar. Therefore, Both K4 and Q3 are planar, making (B) the correct choice.

A) K4 is planar while Q3 is not

C) Q3 is planar while K3 is not

Engineering Mathematics · Discrete Mathematics

Official IIT answer key · IIT Madras · Audited Aug 2026

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GATE CSE 2011 Q17 · MCQ · 1 mark

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

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Key concept

Discrete Mathematics

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How GATE tests Discrete Mathematics

In GATE Computer Science, Discrete Mathematics is heavily tested across mathematical logic, set theory, relations & partial orders/lattices, group theory, combinatorics, and graph theory. Questions evaluate formal reasoning, counterexample construction, and structural counting principles. Over recent years, question formats have transitioned from standard single-choice definitions to multi-select properties (MSQs) and exact integer/combinatorial numerical answers (NATs).

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

Engineering Mathematics · Discrete Mathematics

Official IIT answer key · IIT Madras · Audited Aug 2026

Take topic test

GATE CSE 2011 Q17 · MCQ · 1 mark

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

Select an option to check

Key concept

Discrete Mathematics

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Discrete Mathematics

Full Discrete Mathematics guide →

More on Discrete Mathematics

All 50 questions on Discrete Mathematics →

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

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

Step-by-step verified solution

Check you can still solve Discrete Mathematics under a clock

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More on Discrete Mathematics

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

Step-by-step verified solution

Check you can still solve Discrete Mathematics under a clock

More from GATE CSE 2011

More on Discrete Mathematics

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

Step-by-step verified solution

Check you can still solve Discrete Mathematics under a clock

More from GATE CSE 2011

More on Discrete Mathematics

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

Step-by-step verified solution

Check you can still solve Discrete Mathematics under a clock

More from GATE CSE 2011

More on Discrete Mathematics

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