The distance-regular graphs such that all of its second largest local eigenvalues are at most one

Details The distance-regular graphs such that all of its second largest local eigenvalues are at most one The distance-regular graphs such that all of its second largest local eigenvalues are at most one

2011-02-21

arxiv.org/abs/1102.4292v1

Mathematics

Combinatorics

16 pages, this is submitted to Linear Algebra and Applications

Scientific paper

In this paper, 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 graph
with smallest eigenvalue $-1-\frac{b_1}{2}$.

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