Compression of vertex transitive graphs

Abstract

We consider the lossless compression of vertex transitive graphs. An undirected graph G = (V, E) is called vertex transitive if for every pair of vertices x, y ∈ V , there is an automorphism σ of G, such that σ(x) = y. A result due to Sabidussi, guarantees that for every vertex transitive graph G there exists a graph mG (m is a positive integer) which is a Cayley graph. We propose as the compressed form of G a finite presentation (X, R) , where (X, R) presents the group Γ corresponding to such a Cayley graph mG. On a conjecture, we demonstrate that for a large subfamily of vertex transitive graphs, the original graph G can be completely reconstructed from its compressed representation.