Abstract : A visual cryptography scheme based on a given graph G is a method to distribute a secret image among the vertices of G, the participants, so that a subset of participants can recover the secret image if they contain an edge of G, by stacking their shares, otherwise they can obtain no information regarding the secret image. In this paper a maximal independent sets of the graph G was applied to propose a lower bound on the pixel expansion of visual cryptography schemes with graph access structure  (G ). In addition a lower bound on the pixel expansion of basis matrices C₅ and Peterson graph access structure were presented .