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Let be a finite ring. The bipartite graph associated to elements and cosets of subrings of is a simple undirected graph with vertex set, where is the set of all subrings of, and two vertices and are adjacent if and only if In this study, we investigate some basic properties of the graph. In particular, we investigate some properties of, where is the ring of matrices over Also, we study the diameter of the bipartite graph associated to the quaternion ring