Abstract. Let R be a ring, M be a left and right R-module. We associate a bipartite graph to R-module M of ring R, denoted by ΓR,M as undirected simple graph whose two parts of vertices are R\CR(M) and M \CM(R) and two distinct vertices x and y are adjacent if xy ̸= yx, where CR(M) is the set of elements of R that commute with all elements in M. Some graph theoretical properties of this graph stated in this paper.

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