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An inequality involving the second largest and smallest eigenvalue of a distance-regular graph

An inequality involving the second largest and smallest eigenvalue of a distance-regular graph,10.1016/j.laa.2010.12.032,Linear Algebra and Its Applic

An inequality involving the second largest and smallest eigenvalue of a distance-regular graph   (Citations: 1)
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For a distance-regular graph with second largest eigenvalue (resp., smallest eigenvalue) θ1 (resp., θD) we show that (θ1+1)(θD+1)⩽-b1 holds, where equality only holds when the diameter equals two. Using this inequality we study distance-regular graphs with fixed second largest eigenvalue.
Journal: Linear Algebra and Its Applications - LINEAR ALGEBRA APPL , vol. 434, no. 12, pp. 2404-2412, 2011
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