Visual cryptography scheme on graphs with $m^{*}(G)=۴$

‎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 $m^{*}(G)=۴$ and $\omega (G)=۵$ which $\omega(G)$ is the clique number of graph $G$‎.

Keywords:

‎Secret sharing schemes‎ , ‎Visual cryptography scheme‎ , ‎Graph access structure‎ , ‎Pixel expansion