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math.CO2013
The spectrum and toughness of regular graphs
Sebastian M. Cioabă, Wiseley Wong
In 1995, Brouwer proved that the toughness of a connected -regular graph is at least , where is the maximum absolute value of the non-trivial eigenvalues of .…
math.CO2013
Edge-disjoint spanning trees and eigenvalues of regular graphs
Sebastian M. Cioabă, Wiseley Wong
Partially answering a question of Paul Seymour, we obtain a sufficient eigenvalue condition for the existence of edge-disjoint spanning trees in a regular graph, when $k\in \{2…
math.CO2013
The graphs with all but two eigenvalues equal to
Sebastian M. Cioabă, Willem H. Haemers, Jason Vermette +1
We determine all graphs whose adjacency matrix has at most two eigenvalues (multiplicities included) different from and decide which of these graphs are determined by their…