Matching number and the spectral properties depending on the characteristic polynomial of a graph obtained by means of the adjacency polynomial has many interesting applications in different areas of science. There are some work giving the relation of these two areas. Here the relations between these two notions are considered and several general results giving this relations are obtained. A result given for only unicyclic graphs is generalized. There are some methods for determining the matching number of a graph in literature. Usually nullity, spanning trees and several graph parts are used to do this. Here, as a new method, the conditions for calculating the matching number of a graph by means of the coefficients of the characteristic polynomial of the graph are determined. Finally some results on the matching number of graphs are obtained.

取决于通过邻接多项式获得的图的特征多项式的匹配数和光谱特性在科学的不同领域中具有许多有趣的应用。有一些工作给出了这两个领域的关系。这里考虑了这两个概念之间的关系，并获得了给出该关系的几个一般结果。概括了仅对单圈图给出的结果。有一些方法可以确定文献中图形的匹配数。通常使用无效性，生成树和几个图部分来执行此操作。在此，作为一种新方法，确定了通过图的特征多项式的系数来计算图的匹配数的条件。最后，得到了一些与图的匹配数量有关的结果。