10 papers
Large sets of mutually orthogonal quantum Latin squares
Simeon Ball, Robin Simoens
How large can a set of mutually orthogonal quantum Latin squares (MOQLS) get? We show that a set of n - 2 MOQLS of order n is necessarily classical and construct large non-classica…
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
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…
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…
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…
The minimum weight of the code of intersecting lines in
Sam Adriaensen, Robin Simoens, Leo Storme
We characterise the minimum weight codewords of the -ary linear code of intersecting lines in , , , prime, . If is even, the mini…
Stabiliser codes over fields of even order
Simeon Ball, Edgar Moreno, Robin Simoens
We prove that the natural isomorphism between GF(2^h) and GF(2)^h induces a bijection between stabiliser codes on n quqits with local dimension q=2^h and binary stabiliser codes on…
Cospectral mates for generalized Johnson and Grassmann graphs
Aida Abiad, Jozefien D'haeseleer, Willem H. Haemers +1
We provide three infinite families of graphs in the Johnson and Grassmann schemes that are not uniquely determined by their spectrum. We do so by constructing graphs that are cospe…
On the diameter and zero forcing number of some graph classes in the Johnson, Grassmann and Hamming association scheme
Aida Abiad, Robin Simoens, Sjanne Zeijlemaker
We determine the diameter of generalized Grassmann graphs and the zero forcing number of some generalized Johnson graphs, generalized Grassmann graphs and the Hamming graphs. Our w…