The matching polynomial of a graph has coefficients that give the number of matchings in the graph. In this paper, we determine all connected graphs on eight vertices whose matching polynomials have only integer zeros. A graph is matching integral if the zeros of its matching polynomial are all integers. We show that there are exactly two matching integral graphs on eight vertices.

中文翻译：

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在匹配积分图上

图的匹配多项式的系数给出了图中的匹配次数。在本文中，我们确定八个顶点上的所有连接图，这些顶点的匹配多项式只有整数零。如果图的匹配多项式的零都是整数，则它是匹配的积分。我们证明在八个顶点上恰好有两个匹配的积分图。