186 citations · 238 across the 42 of their papers we have counts for
6 papers · 1 filter
There does not exist a distance-regular graph with intersection array
Jack H. Koolen, Quaid Iqbal, Jongyook Park +1
In this paper we will show that there does not exist a distance-regular graph with intersection array . We first show that a local graph of doe…
On the order of regular graphs with fixed second largest eigenvalue
Jae Young Yang, Jack H. Koolen
Let be the maximum number of vertices of a connected -regular graph with second largest eigenvalue at most . The Alon-Boppana Theorem implies that is fini…
Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature
David Cushing, Supanat Kamtue, Jack Koolen +3
We introduce the notion of Bonnet-Myers and Lichnerowicz sharpness in the Ollivier Ricci curvature sense. Our main result is a classification of all self-centered Bonnet-Myers shar…
On the integrability of strongly regular graphs
Jack H. Koolen, Masood Ur Rehman, Qianqian Yang
Koolen et al. showed that if a connected graph with smallest eigenvalue at least has large minimal valency, then it is -integrable. In this paper, we will prove that a lowe…
On a characterization of the Grassmann graphs
Alexander L. Gavrilyuk, Jack H. Koolen
In 1995, Metsch showed that the Grassmann graph of diameter is characterized by its intersection numbers with the following possible exceptions: (-) or…
On graphs with smallest eigenvalue at least -3 and their lattices
Jack H. Koolen, Jae Young Yang, Qianqian Yang
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…