4 papers
Thirty-six quantum officers are entangled
Simeon Ball, Robin Simoens
There exist pairs of orthogonal Latin squares of any order n except if n=2 or n=6 [Bose, Shrikhande and Parker, 1960]. In particular, the problem of Euler's thirty-six officers doe…
The edge-isoperimetric number of graphs and their powers: approaches from spectral graph theory, optimization and finite geometry
Aida Abiad, Nils van de Berg, Emanuel Juliano +4
We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph p…
Counting cospectral graphs obtained via switching
Aida Abiad, Nils Van de Berg, Robin Simoens
Switching is an operation on a graph that does not change the spectrum of the adjacency matrix, thus producing cospectral graphs. An important activity in the field of spectral gra…
Switching methods of level 2 for the construction of cospectral graphs
Aida Abiad, Nils van de Berg, Robin Simoens
A switching method is a graph operation that results in cospectral graphs (graphs with the same spectrum). Work by Wang and Xu [Discrete Math. 310 (2010)] suggests that most cospec…