186 citations · 238 across the 42 of their papers we have counts for
47 papers
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,…
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 , any geometric distance-regular graph with smallest eigenvalue , diameter …
Comparing classes of highly symmetric graphs: From -arc-transitive to -distance-transitive
Wei Jin, Jack H. Koolen, Chenhui Lv
A -distance-transitive graph is a vertex-transitive graph whose vertex stabilizer is transitive on both the first- and second-step neighborhoods. This concept simultaneously gen…
Edge-connectivity of graphs with non-negative Bakry-Émery curvature and amply regular graphs
Kaizhe Chen, Jack H. Koolen, Shiping Liu
We establish a sharp edge-connectivity estimate for graphs with non-negative Bakry-Émery curvature. This leads to a geometric criterion for the existence of a perfect matching. Pre…
An improved bound for strongly regular graphs with smallest eigenvalue
Jack Koolen, Chenhui Lv, Greg Markowsky +1
In 1979, Neumaier gave a bound on in terms of and , where is the smallest eigenvalue of a primitive strongly regular graph, unless the graph in question belongs to…
On co-edge-regular graphs with 4 distinct eigenvalues
Hong-Jun Ge, Jack H. Koolen
Tan et al. conjectured that connected co-edge-regular graphs with four distinct eigenvalues and fixed smallest eigenvalue, when having sufficiently large valency, belong to two dif…