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Maximal Energy Graphs

- J. Koolen, V. Moulton
- Mathematics, Computer Science
- Adv. Appl. Math.
- 2001

TLDR

Distance-regular graphs

This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in… Expand

A New Family of Distance-Regular Graphs with Unbounded Diameter

We construct distance-regular graphs with the same-classical-parameters as the Grassman graphs on the e-dimensional subspaces of a (2e+1)-dimensional space over an arbitrary finite field. This… Expand

Open problems in the spectral theory of signed graphs

- F. Belardo, S. Cioaba, J. Koolen, Jianfeng Wang
- Computer Science, Mathematics
- Art Discret. Appl. Math.
- 9 July 2019

TLDR

On the Hyperbolicity of Chordal Graphs

- G. Brinkmann, J. Koolen, V. Moulton
- Mathematics
- 1 June 2001

Abstract. The hyperbolicity
$ \delta^* \ge 0 $ of a metric space in Gromov's sense can be viewed as a measure of how "tree-like" the space is, since those spaces for which
$ \delta^* = 0 $ holds… Expand

On the connectedness of the complement of a ball in distance-regular graphs

An important property of strongly regular graphs is that the second subconstituent of any primitive strongly regular graph is always connected. Brouwer asked to what extent this statement can be… Expand

On graphs with smallest eigenvalue at least -3 and their lattices.

- J. Koolen, Jae Young Yang, Qianqian Yang
- Mathematics
- 2 April 2018

In this paper, we show that a connected graph with smallest eigenvalue at least -3 and large enough minimal degree is 2-integrable. This result generalizes a 1977 result of Hoffman for connected… Expand

An improvement of the Ivanov bound

AbstractLet Γ be a distance-regular graph of diameterd, valencyk andr=max{i|(ci,bi)=(c1,b1)}. In this paper, we prove that
$$d< \frac{1}{2}k^3 r.$$

On the multiplicity of eigenvalues of distance-regular graphs

Abstract We rule out the infinite series of feasible intersection array {μ(2μ + 1), (μ − 1)(2μ + 1), μ2, μ; 1, μ, μ(μ − 1), μ(2μ + 1), μ ⩾ 2}.

Tight Distance-Regular Graphs

- A. Jurisic, J. Koolen, Paul M. Terwilliger
- Mathematics
- 1 September 2000

AbstractWe consider a distance-regular graph Γ with diameter d ≥ 3 and eigenvalues k = θ0 > θ1 > ... > θd. We show the intersection numbers a1, b1 satisfy
$$\left( {\theta _1 + \frac{k}{{a_1 + 1}}}… Expand

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