Convergence results on the stable states of a Gravitational Swarm solving the Graph Coloring Problem

A Gravitational Swarm (GS) is a collection of agents endowed with mass moving in the space under the forces generated by their gravitational attraction. Under appropriate interpretations, the stable global states of this system can be used as solution to some problem, specifically we provide a mapping of the Graph Coloring Problem (GCP) into a GS, so that stable swarm global states correspond to GCP solutions. This paper provides formal proofs of some conditions ensuring the convergence GS to solutions of the GCP on undirected graphs with a given number of colors. We provide also encouraging results of computational experiments where GS achieves competitive performance of the approach compared with state-of-the-art GCP solving algorithms.