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

Abstract

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.

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

References in corpus (2)

• Shilla distance-regular graphs
• There are only finitely many distance-regular graphs of fixed valency greater than two

Cited by in corpus (2)

• Distance-regular graph with large a1 or c2
• On electric resistances for distance-regular graphs