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Let G n be a simple graph with n vertices. Gutman and Wagner founded the theory of random graphs, they introduced the matching energy of the graph G n , which was defined as the sum of the absolute values of the eigenvalues of the matching polynomial of the graph G n . For the Erdös-Rényi type random graph G n,p of order n with a fixed probability p, where p is a real number greater than zero and less than 1, that is, the graph G on n vertices by connecting two vertices with probability p(e),doi:10.4310/pamq.2015.v11.n3.a1 fatcat:xglb7na3yfe4bem544qwon5ase