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

Jack H. Koolen; Hyonju Yu

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

Combinatorics 2011-02-22 v1

Authors: Jack H. Koolen , Hyonju Yu

Abstract

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 $-1-\frac{b_1}{2}$ .

Keywords

distance-regular graphs local eigenvalues second largest eigenvalue smallest eigenvalue graph classification

Cite

@article{arxiv.1102.4292,
  title  = {The distance-regular graphs such that all of its second largest local eigenvalues are at most one},
  author = {Jack H. Koolen and Hyonju Yu},
  journal= {arXiv preprint arXiv:1102.4292},
  year   = {2011}
}

Comments

16 pages, this is submitted to Linear Algebra and Applications

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