VISUAL CRYPTOGRAPHY SCHEME ON GRAPHS WITH m∗(G) = 4

Let g = (v, e) be a connected graph and γ(g) be the strong access structure where obtained from graph g. a visual cryptography scheme (vcs) for a set p of participants is a method to encode a secret image such that any pixel of this image change to m subpixels and only qualified sets can recover the secret image by stacking their shares. the value of m is called the pixel expansion and the minimum value of the pixel expansion of a vcs for γ(g) is denoted by m∗ (g). in this paper we obtain a characterization of all connected graphs g with m∗ (g) = 4 and ω(g) = 5 which ω(g) is the clique number of graph g.