Visual cryptography scheme on graphs with $m^{*}(G)=4$

Abstract

‎Let $G=(V,E)$ be a connected graph and $Gamma (G)$ 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 $Gamma (G)$ is denoted by $m^{*}(G)$‎. ‎In this paper we obtain a characterization of all connected graphs $G$ with $m^{*}(G)=4$ and $omega (G)=5$ which $omega(G)$ is the clique number of graph $G$‎.