GATE 2023 CS – Question 30
Let A be the adjacency matrix of the graph with vertices {1, 2, 3, 4, 5}. [Figure: a graph on vertices 1-5.] Let $\lambda_1,\lambda_2,\lambda_3,\lambda_4,\lambda_5$ be the five eigenvalues of A. Note that these eigenvalues need not be distinct. The value of $\lambda_1+\lambda_2+\lambda_3+\lambda_4+\lambda_5$ = ______.
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Correct answer: 0
Explanation
The sum of eigenvalues equals the trace of A. A simple graph has no self-loops, so the diagonal is all zeros and the sum is 0.