Abstract
The matching energy is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph,which was firstly proposed by Gutman and Wagner(The matching energy of a graph,Discrete Appl.Math.2012(160):2177-2187).And they showed that the complete graph K_n had maximum matching energy in all graphs on n vertices.In this paper,among all graphs on n vertices,the graphs with i-th maximal matching energy are completely characterized,where i= 2,3,...,16.
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