GATE CSE 2024 Session 2 Q17: Graph whose adjacency matrix is its own inverse
- Engineering Mathematics
- 1 mark
- MCQ
- −1/3 if wrong
Question
Let be the adjacency matrix of a simple undirected graph . Suppose is its own inverse. Which one of the following statements is always TRUE?
Try it: multiple choice: exactly one correct option
Wrong answer costs 1/3 mark in GATE.
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Answer: B (official GATE 2024 final answer key)
Concept used: counts walks of length 2 from to ; constrains degrees.
First step: is the degree of vertex , so every vertex has degree 1, and no two vertices share a neighbour.
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Source: official GATE 2024 Session 2 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key
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