Engineering Mathematics · Graph Theory
Official IIT answer key · IIT Roorkee · Audited Aug 2026
GATE CSE 2026 Set 2 Q8 · MCQ · 2 marks
Figures (i) and (ii) represent intercity highway systems. The black dots represent cities and the line segments between them represent intercity highways. A salesperson needs to make a trip. She needs to start from a city, visit each of the remaining cities exactly once, and finally return to the same city from which she started.
Key concept
Topic notes
In GATE CS, graph theory under Engineering Mathematics emphasizes structural properties, algebraic relationships, and topological invariants of simple undirected graphs. Questions frequently evaluate planar graph relationships using Euler's formula, chromatic numbers and edge coloring bounds (Vizing's theorem, independent set bounds), and degree-based properties (Handshaking lemma, Havel-Hakimi theorem). The focus has steadily migrated from direct formula applications to structural reasoning and algebraic characterizations such as matrix powers.
Full Graph Theory guide →Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.
