中文摘要：

图的完美匹配的熵是指完美匹配数取对数后与顶点数的一半的比值.通过完美匹配数的精确表达式讨论了在环面上的四边形网格图的完美匹配的熵,从而证明了在不同边界条件下的四边形网格图的完美匹配的熵均为0.583 1.

英文摘要：

The free energy of per perfect matching is named the entropy of perfect matching of a graph. In this paper, the entropies of perfect matching of the quadrilateral lattices embedded on the torus are discussed by their expressions for the number of perfect matching. What＇s more, it is obtained that the entropies of perfect matching of the quadrilateral lattices embedded on the different boundary are e- qual, i.e. 0.583 1.