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

‎Let G=(V,E)G=(V,E) be a connected graph and Γ(G)Γ(G) be the strong access structure where obtained from graph GG‎. ‎A visual cryptography scheme (VCS) for a set PP of participants is a method to encode a secret image such that any pixel of this image change to mm subpixels and only qualified sets can recover the secret image by stacking their shares‎. ‎The value of mm is called the pixel expansion and the minimum value of the pixel expansion of a VCS for Γ(G)Γ(G) is denoted by m∗(G)m∗(G)‎. ‎In this paper we obtain a characterization of all connected graphs GG with m∗(G)=4m∗(G)=4 and ω(G)=5ω(G)=5 which ω(G)ω(G) is the clique number of graph GG‎.