55 citations · 99 across the 10 of their papers we have counts for
10 papers · 1 filter
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…
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…
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…
A short proof of the odd-girth theorem
Edwin R. van Dam, Miquel Angel Fiol
Recently, it has been shown that a connected graph with distinct eigenvalues and odd-girth is distance-regular. The proof of this result was based on the spectral…