Generating Integral Graphs Using PRACE Research Infrastructure

In this white paper we report the work that was done on the problem of generation combinatorial structures with some rare invariant properties. These combinatorial structures are connected integral graphs. All (588) of such graphs of order 1 ≤ n ≤ 12 are known. The main goal of this work was to reduce the time of generation by distributing graph generators over hosts in PRACE-RI, and to reduce the time of sieving integral graphs by applying eigenvalue calculation in GPGPU device using the OpenCL technique. This work is also a study of how to minimize the overhead connected with using OpenCL kernels.