55 citations · 99 across the 10 of their papers we have counts for
5 papers · 2 filters
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…
On perturbations of almost distance-regular graphs
Cristina Dalfó, Edwin R. van Dam, Miquel Angel Fiol
In this paper we show that certain almost distance-regular graphs, the so-called -punctually walk-regular graphs, can be characterized through the cospectrality of their perturb…
On almost distance-regular graphs
Cristina Dalfó, Edwin R. van Dam, Miquel Angel Fiol +2
Distance-regular graphs are a key concept in Algebraic Combinatorics and have given rise to several generalizations, such as association schemes. Motivated by spectral and other al…
Graphs whose normalized Laplacian has three eigenvalues
Edwin R. van Dam, Gholamreza Omidi
We give a combinatorial characterization of graphs whose normalized Laplacian has three distinct eigenvalues. Strongly regular graphs and complete bipartite graphs are examples of…
An odd characterization of the generalized odd graphs
Edwin R. van Dam, Willem H. Haemers
We show that any connected regular graph with distinct eigenvalues and odd-girth is distance-regular, and in particular that it is a generalized odd graph.