University of Isfahan Transactions on Combinatorics 2251-8657 8 2 2019 06 01 Visual cryptography scheme on graphs with $m^{*}(G)=4$ 53 66 23300 10.22108/toc.2019.113671.1599 EN Mahmood Davarzani Faculty of Mathematics and Computer Science, Kharazmi University, Tehran, Iran. Journal Article 2018 10 28 ‎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 $G$‎. https://toc.ui.ac.ir/article_23300_7e7b355bb19939b05f34a1a4f0a374b3.pdf