8 papers
Signed graphs with fixed smallest eigenvalue at least and their lattices
Meng-Yue Cao, Jack H. Koolen, Jing-Yuan Liu +1
In this paper, we consider connected signed graphs with smallest eigenvalue at least for a small positive constant . We prove that if such a signed gr…
Co-edge-regular graphs with four eigenvalues and unbounded coherent rank
Edwin R. van Dam, Hong-Jun Ge, Jack H. Koolen
In the regular three-eigenvalue setting, spectral complexity and coherent-algebraic complexity coincide: a connected regular graph has exactly three distinct eigenvalues if and onl…
Amply regular graphs with close to half the valency and group divisible designs
Wei Jin, Jack H. Koolen, Chenhui Lv
In this paper, we classify connected amply regular graphs with diameter and parameters satisfying , where is odd. We prove…
Almost amorphic association schemes
Edwin van Dam, Jack H. Koolen, Yanzhen Xiong
An association scheme is called amorphic if every possible fusion of relations gives rise to another association scheme. In earlier work, we showed that if an association scheme ha…
Geometry of ample/lopsided sets
Hans--Jürgen Bandelt, Victor Chepoi, Andreas Dress +1
Lopsided sets were introduced by Jim Lawrence in 1983 when he studied the subsets of that encode the intersection pattern of a convex set with the orthants of ${\…
A family of Neumaier graphs containing examples with exactly five eigenvalues
Bart De Bruyn, Rhys J. Evans, Sergey Goryainov +1
A Neumaier graph is an edge-regular graph with a regular clique. Such a graph is said to have parameters if it is a -regular graph on vertices having a clique…