GATE CS 2022 Set 1 — Question 50

MSQ+2 / -0HardGraph ColoringGraph Theory (Math)Engineering MathematicsEuler & Hamiltonian PathsGraph Terminology (Degree, Paths, Cycles)

Engineering Mathematics → Graph Theory (Math) → Euler & Hamiltonian Paths

Last updated 5 September 2026

Question

The following simple undirected graph is referred to as the Peterson graph. Which of the following statements is/are TRUE?

Correct answer (A) The chromatic number of the graph is 3.; (B) The graph has a Hamiltonian path.; (C) The following graph is isomorphic to the Peterson graph. [figure] Solution Option (A): The Peterson graph is 3-colorable. Its chromatic number is 3. TRUE. Option (B): The Peterson graph has a Hamiltonian path (a path visiting every vertex exactly once) but does not have a Hamiltonian cycle. TRUE. Option (C): The graph shown is a known isomorphic representation of the Peterson graph (often drawn as a circle with chords or a bipartite-like structure with specific connections). TRUE. Option (D): The maximum independent set size of the Peterson graph is 4. FALSE. Correct Options: A, B, C. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (A) The chromatic number of the graph is 3.; (B) The graph has a Hamiltonian path.; (C) The following graph is isomorphic to the Peterson graph. [figure] Solution Option (A): The Peterson graph is 3-colorable. Its chromatic number is 3. TRUE. Option (B): The Peterson graph has a Hamiltonian path (a path visiting every vertex exactly once) but does not have a Hamiltonian cycle. TRUE. Option (C): The graph shown is a known isomorphic representation of the Peterson graph (often drawn as a circle with chords or a bipartite-like structure with specific connections). TRUE. Option (D): The maximum independent set size of the Peterson graph is 4. FALSE. Correct Options: A, B, C.

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