Hyperset Individualisation for the Graph Isomorphism Problem

In this work, we propose a novel approach for graph canonisation called Hyperset Individualisation (HI), combining node-individualisation and bisimulation reduction on a set-theoretic framework in an effort to tackle the Graph Isomorphism problem on simple graphs. Building on this idea, we define a variant of HI which enhances its expressiveness by integrating the structural information provided by points (PHI); moreover, we define and study two non-equivalent k-dimensional versions of the algorithm (HIE and HIA). Finally, we present an iterative refinement framework based on rendering of node partitions by means of atoms.