The most important technologies in modern society are the information security; it is founded to provide a protection to the transmitted data. Secret sharing scheme is one of the methods designated to protect the secret data. It is a method that allows a secret to be shared among a set of participants in such a way that only qualified subsets of them can recover the secret by pooling their share together, but no less sets can do that. Many mathematical structures are used to create a secret sharing scheme; the one that based on graph access structure is the most widely used structure. In this paper, a new horizon for the construction of the perfect secret sharing schemes of rank 2 and 3 is opened by proposing of a new algorithm to construct a uniform access structure in a connected, simple, undirected, r-regular graph G.This has been done by introducing for the first time the minimum independent dominating set of vertices in a graph. The efficiency of this method is deduced to prove that the proposed method has an improvement over other previous methods.