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arXiv · 0907.4906

Inductive Construction of 2-Connected Graphs for Calculating the Virial Coefficients

E. Androulaki·S. Lambropoulou·I. G. Economou·J. H. Przytycki
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Abstract

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.

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E. Androulaki, S. Lambropoulou, I. G. Economou, J. H. Przytycki. 2010-07-15. Inductive Construction of 2-Connected Graphs for Calculating the Virial Coefficients. https://doi.org/10.1088/1751-8113%2F43%2F31%2F315004

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