186 citations · 405 across the 30 of their papers we have counts for
31 papers
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…
The Hoffman program for mixed graphs
Yuantian Yu, Edwin R. van Dam
We consider Hoffman's program about the limit points of the spectral radius of the Hermitian adjacency matrix of mixed graphs. In particular, we determine all mixed graphs without…
Characterizations of amorphic schemes and fusions of pairs
Edwin R. van Dam, Jack H. Koolen, Yanzhen Xiong
An association scheme is called amorphic if every possible fusion of relations gives rise to a fusion scheme. We call a pair of relations fusing if fusing that pair gives rise to a…
Rainbow Hamiltonicity and the spectral radius
Yuke Zhang, Edwin R. van Dam
Let be a family of graphs of order with the same vertex set. A rainbow Hamiltonian cycle in is a cycle that visits each vertex p…
Symmetry in complex unit gain graphs and their spectra
Pepijn Wissing, Edwin R. van Dam
Complex unit gain graphs may exhibit various kinds of symmetry. In this work, we explore structural symmetry, spectral symmetry and sign-symmetry in such graphs, and their respecti…
Matching extension and distance spectral radius
Yuke Zhang, Edwin R. van Dam
A graph is called -extendable if each -matching can be extended to a perfect matching. We give spectral conditions for the -extendability of graphs and bipartite graphs us…
Spectra of power hypergraphs and signed graphs via parity-closed walks
Lixiang Chen, Edwin R. van Dam, Changjiang Bu
The -power hypergraph is the -uniform hypergraph that is obtained by adding new vertices to each edge of a graph , for . A parity-closed walk in…
All eigenvalues of the power hypergraph and signed subgraphs of a graph
Lixiang Chen, Edwin R. van Dam, Changjiang Bu
We show how all eigenvalues of a power hypergraph can be generated from the eigenvalues of signed subgraphs of the underlying graph . This fixes an incorrect statement…
Signless Laplacian Estrada index and Laplacian Estrada index of uniform hypergraphs
Cunxiang Duan, Edwin R. van Dam, Ligong Wang
We generalize the notions of Laplacian and signless Laplacian Estrada index to uniform hypergraphs. For an -uniform hypergraph we derive an order trace formula of the…
Pseudo-Geometric Strongly Regular Graphs with a Regular Point
Edwin van Dam, Krystal Guo
We study pseudo-geometric strongly regular graphs whose second subconstituent with respect to a vertex is a cover of a strongly regular graph or a complete graph. By studying the s…
On bipartite distance-regular Cayley graphs with small diameter
Edwin R. van Dam, Mojtaba Jazaeri
We study bipartite distance-regular Cayley graphs with diameter three or four. We give sufficient conditions under which a bipartite Cayley graph can be constructed on the semidire…
Spectral Fundamentals and Characterizations of Signed Directed Graphs
Pepijn Wissing, Edwin R. van Dam
The spectral properties of signed directed graphs, which may be naturally obtained by assigning a sign to each edge of a directed graph, have received substantially less attention…
Partially metric association schemes with a multiplicity three
Edwin R. van Dam, Jack H. Koolen, Jongyook Park
An association scheme is called partially metric if it has a connected relation whose distance-two relation is also a relation of the scheme. In this paper we determine the symmetr…
Laplacian spectral characterization of roses
Changxiang He, Edwin R. van Dam
A rose graph is a graph consisting of cycles that all meet in one vertex. We show that except for two specific examples, these rose graphs are determined by the Laplacian spectrum,…
Distance-regular Cayley graphs with least eigenvalue
Alireza Abdollahi, Edwin van Dam, Mojtaba Jazaeri
We classify the distance-regular Cayley graphs with least eigenvalue and diameter at most three. Besides sporadic examples, these comprise of the lattice graphs, certain trian…
Directed strongly walk-regular graphs
Edwin R. van Dam, Gholamreza Omidi
We generalize the concept of strong walk-regularity to directed graphs. We call a digraph strongly -walk-regular with if the number of walks of length from a…
New bounds for the max--cut and chromatic number of a graph
Edwin R. van Dam, Renata Sotirov
We consider several semidefinite programming relaxations for the max--cut problem, with increasing complexity. The optimal solution of the weakest presented semidefinite program…
Distance-regular graphs
Edwin R. van Dam, Jack H. Koolen, Hajime Tanaka
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 s…
Graphs with many valencies and few eigenvalues
Edwin R. van Dam, Jack H. Koolen, Zheng-jiang Xia
Dom de Caen posed the question whether connected graphs with three distinct eigenvalues have at most three distinct valencies. We do not answer this question, but instead construct…
The Laplacian spectral excess theorem for distance-regular graphs
Edwin R. van Dam, Miquel Angel Fiol
The spectral excess theorem states that, in a regular graph G, the average excess, which is the mean of the numbers of vertices at maximum distance from a vertex, is bounded above…
Some Spectral and Quasi-Spectral Characterizations of Distance-Regular Graphs
A. Abiad, E. R. van Dam, M. A. Fiol
In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the i…
Semidefinite programming and eigenvalue bounds for the graph partition problem
Edwin R. van Dam, Renata Sotirov
The graph partition problem is the problem of partitioning the vertex set of a graph into a fixed number of sets of given sizes such that the sum of weights of edges joining differ…
Geometric aspects of 2-walk-regular graphs
Marc Cámara, Edwin R. van Dam, Jack H. Koolen +1
A -walk-regular graph is a graph for which the number of walks of given length between two vertices depends only on the distance between these two vertices, as long as this dist…
On bounding the bandwidth of graphs with symmetry
Edwin R. van Dam, Renata Sotirov
We derive a new lower bound for the bandwidth of a graph that is based on a new lower bound for the minimum cut problem. Our new semidefinite programming relaxation of the minimum…