GATE CSE 2022 Q37: Counting triangles from the trace of A³
- Engineering Mathematics
- 2 marks
- MCQ
- −2/3 if wrong
Question
Consider a simple undirected unweighted graph with at least three vertices. If is the adjacency matrix of the graph, then the number of 3-cycles in the graph is given by the trace of
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Answer: D (official GATE 2022 final answer key)
Concept used: counts closed walks of length 3 from vertex .
First step: Count how many closed 3-walks one triangle produces: 3 starting vertices × 2 directions.
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Source: official GATE 2022 CS question paper and final answer key, organised by IIT Kharagpur. Question paper · Answer key
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