The enumerative problem of spanning trees of graphs is one of the fundamental problems in the field of graph theory, which has attracted the attention of mathematicians and physicists. For a connected graph , let be a spanning tree of . In this paper, we call to be a - of if contains a perfect matching. Recently, Li and Yan (Applied Mathematics and Computation, 456 (2023), 128125.) gave an explicit expression for the number of pm-trees in linear hexagonal chains on the plane, cylinder and Möbius strip, respectively. In this paper, we extend the results above and obtain the explicit formula for the number of pm-trees in linear polygonal chains with polygons of vertices on the plane, cylinder and Möbius strip, respectively.

中文翻译：

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包含线性多边形链中完美匹配的生成树的枚举


图的生成树的枚举问题是图论领域的基本问题之一，引起了数学家和物理学家的关注。对于连通图，设 为 的生成树。在本文中，我们称其为-if 包含完美匹配。最近，Li和Yan (Applied Mathematics and Computation, 456 (2023), 128125.)分别给出了平面、圆柱和莫比乌斯带上线性六边形链中pm树数量的明确表达式。在本文中，我们对上述结果进行了扩展，得到了顶点多边形分别位于平面、圆柱和莫比乌斯带上的线性多边形链中 pm 树数量的显式公式。