186 citations · 405 across the 30 of their papers we have counts for
4 papers · 1 filter
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…