From the 1 of 7 linked papers with an AI index.
7 papers
Large sets of mutually orthogonal quantum Latin squares
Simeon Ball, Robin Simoens
The paper studies the maximum size of sets of mutually orthogonal quantum Latin squares, proving that any set of n‑2 such squares of order n must be classical and constructing larg…
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…
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…
Design switching on graphs
Ferdinand Ihringer, Robin Simoens
We show that each (r, lambda)-design yields a class of switching methods that can be used to produce cospectral graphs. We use this to explain several specific switching methods su…