图的极大匹配能(英文)

On the maximal matching energy of graphs

Gutman和Wagner(The matching energy of a graph,Discrete Appl.Math.2012(160):2177-2187)首次提出了匹配能的定义,即:图的匹配多项式的所有特征根的绝对值之和称为图的匹配能.他们证明了在n个顶点的图中,完全图Kn有最大匹配能.本文完全刻画了具有第二大至第十六大匹配能的图.

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 Kn 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.