J. Koolen

activity

20242026

collaborators

11 papers

math.CO2026

On the Smallest Eigenvalues and Quantum Chromatic Numbers of Hamming Graphs and Generalizations

Yu Ning, Jack H. Koolen, Xiande Zhang

The smallest eigenvalues of (distance-j) Hamming graphs with distance parameter j at least half the length were completely determined by Brouwer et al. (2018). In the present work,…

math.CO2026

On the characterization of geometric distance-regular graphs

Chenhui Lv, Jack H. Koolen

In 2010, Koolen and Bang proposed the following conjecture: For a fixed integer $m \geq 2$ , any geometric distance-regular graph with smallest eigenvalue $- m$ , diameter $D \geq 3$ …

math.CO2026

Towards a classification of $1$ -homogeneous distance-regular graphs with positive intersection number $a_{1}$

Jack H. Koolen, Mamoon Abdullah, Brhane Gebremichel +1

Let $I^$ be a graph with diameter at least two. Then $I^$ is said to be $1$ -homogeneous (in the sense of Nomura) whenever for every pair of adjacent vertices $x$ and $y$ in $I^$ , t…

math.CO2026

An improved bound for strongly regular graphs with smallest eigenvalue $- m$

Jack Koolen, Chenhui Lv, Greg Markowsky +1

In 1979, Neumaier gave a bound on $I^»$ in terms of $m$ and $I^¼$ , where $- m$ is the smallest eigenvalue of a primitive strongly regular graph, unless the graph in question belongs t…

math.CO2025

A Bose-Laskar-Hoffman theory for $I^¼$ -bounded graphs with fixed smallest eigenvalue

Jack H. Koolen, Hong-Jun Ge, Chenhui Lv +1

In 2018, by Ramsey and Hoffman theory, Koolen, Yang, and Yang presented a structural result on graphs with smallest eigenvalue at least $- 3$ and large minimum degree. In this study…

math.CO2025

Bounding the parameter $I^^{2}$ of a distance-regular graph with classical parameters

Chenhui Lv, Jack H. Koolen

Let $I^$ be a distance-regular graph with classical parameters $(D, b, I^\pm, I^^{2})$ satisfying $b \geq 2$ and $D \geq 3$ . Let $r = 1 + b + b^{2} + \dots + b^{D - 1}$ . In 1999, K. Metsch showed that t…

On the Smallest Eigenvalues and Quantum Chromatic Numbers of Hamming Graphs and Generalizations

On the characterization of geometric distance-regular graphs

Towards a classification of 1-homogeneous distance-regular graphs with positive intersection number a1​

An improved bound for strongly regular graphs with smallest eigenvalue −m

A Bose-Laskar-Hoffman theory for I^¼-bounded graphs with fixed smallest eigenvalue

Bounding the parameter I^2 of a distance-regular graph with classical parameters

Towards a classification of $1$ -homogeneous distance-regular graphs with positive intersection number $a_{1}$

An improved bound for strongly regular graphs with smallest eigenvalue $- m$

A Bose-Laskar-Hoffman theory for $I^¼$ -bounded graphs with fixed smallest eigenvalue

Bounding the parameter $I^^{2}$ of a distance-regular graph with classical parameters