3 papers
math.CO2021
Graph toughness from Laplacian eigenvalues
Xiaofeng Gu, Willem H. Haemers
The toughness of a graph is defined as , in which the minimum is taken over all such that is disconnected, wher…
math.CO2020
Spectral conditions for graph rigidity in the Euclidean plane
Sebastian M. Cioabă, Sean Dewar, Xiaofeng Gu
Rigidity is the property of a structure that does not flex. It is well studied in discrete geometry and mechanics, and has applications in material science, engineering and biologi…
math.CO2016
Connectivity, toughness, spanning trees of bounded degree, and the spectrum of regular graphs
Sebastian M. Cioabă, Xiaofeng Gu
In this paper, we present some new results describing connections between the spectrum of a regular graph and its generalized connectivity, toughness, and the existence of spanning…