This is an exercise from a textbook. I have no clue how to start this .
If G is a graph and $\lambda$ is an eigenvalues of G then prove : $$|\lambda|\le\Delta(G)$$
2026-03-28 17:05:49.1774717549
For lambda eigenvalue of G , how to prove this statement
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If $A$ is an adjacency matrix of $G$ and $|\lambda|>\Delta(G)$ then $A-\lambda I$ is a strictly diagonally dominant matrix, so it is non-singular by Levy–Desplanques theorem, that is $\lambda$ is not an eigenvalue of $A$.