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In this paper, we classify distance regular graphs such that all of itssecond largest local eigenvalues are at most one. Also we discuss theconsequences for the smallest eigenvalue of a distance-regular graph. Theseextend a result by the first author, who classified the distance-regular graphwith smallest eigenvalue $-1-\frac{b_1}{2}$.

The distance-regular graphs such that all of its second largest local eigenvalues are at most one