An inequality involving the second largest and smallest eigenvalue of a distance-regular graph
classification
🧮 math.CO
keywords
eigenvaluedistance-regularlargestsecondgraphholdsinequalityresp
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For a distance-regular graph with second largest eigenvalue (resp. smallest eigenvalue) \mu1 (resp. \muD) we show that (\mu1+1)(\muD+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.
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