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

Details 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

2010-04-07

arxiv.org/abs/1004.1056v1

Mathematics

Combinatorics

15 pages, this is submitted to Linear Algebra and Applications.

Scientific paper

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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