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The distance-regular graphs such that all of its second largest local eigenvalues are at most one. (English)
Linear Algebra Appl. 435, No. 10, 2507-2519 (2011).
Summary: We classify distance regular graphs such that all of its second largest local eigenvalues are at most one. Also we discuss the consequences for the smallest eigenvalue of a distance-regular graph. These extend a result by the first author, who classified the distance-regular graphs with smallest eigenvalue $-1-\frac{b_1}2$.