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GATE 2011 CS (CS1) – Question 27

Engineering Mathematics · Discrete Mathematics: Graphs (Connectivity, Matching, Colouring) · 1 mark · Multiple choice

The drawings show complete graph K₄ and cube graph Q₃. Which is true?

Diagram for GATE 2011 CS (CS1) question 27
  1. K₄ planar, Q₃ not planar
  2. Both planar
  3. Q₃ planar, K₄ not planar
  4. Neither planar

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Show answer and explanation

Correct answer: (B) Both planar

Explanation

Crossings in a particular drawing do not establish nonplanarity. K₄ embeds as an outer triangle with the fourth vertex inside. Q₃ embeds as two nested squares with corresponding corners connected. Both have crossing-free embeddings, B.

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