Graph access structures with optimal pixel expansion three

Let G=(V,E)G=(V,E) be a graph without isolated vertices. Let Γ(G)Γ(G) denote the strong access structure whose basis is the edge set E   and let m⁎(G)m⁎(G) denote the optimal pixel expansion of a visual cryptography scheme for Γ(G)Γ(G). In this paper we obtain a characterization of all connected graphs G   with m⁎(G)=3m⁎(G)=3.