计算维里系数的2-连通图的归纳构造
Inductive Construction of 2-Connected Graphs for Calculating the Virial Coefficients
摘要：
本文给出了从n-1阶简单2-连通图集合中，通过边的剖分和顶点的添加两种操作，系统地构造所有n阶简单2-连通图的方法。我们的研究动机来自非理想气体理论，更具体地说，来自维里状态方程。维里状态方程中的系数是标号2-连通图上的和，这是统计力学的一个已知结果。这些图形对应于粒子簇。因此，从理论上讲，任何阶维里系数都可以用2-连通图计算前一阶维里系数。我们的主要结果给出了一个通过归纳顶点数构造简单2-连通图的方法。此外，我们使用的两个操作保持了图和粒子簇之间的对应关系。
英文摘要：
In this paper we give a method for constructing systematically all simple 2-connected graphs with n vertices from the set of simple 2-connected graphs with n-1 vertices, by means of two operations: subdivision of an edge and addition of a vertex. The motivation of our study comes from the theory of non-ideal gases and, more specifically, from the virial equation of state. It is a known result of Statistical Mechanics that the coefficients in the virial equation of state are sums over labelled 2-connected graphs. These graphs correspond to clusters of particles. Thus, theoretically, the virial coefficients of any order can be calculated by means of 2-connected graphs used in the virial coefficient of the previous order. Our main result gives a method for constructing inductively all simple 2-connected graphs, by induction on the number of vertices. Moreover, the two operations we are using maintain the correspondence between graphs and clusters of particles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
