Inductive Construction of 2-Connected Graphs for Calculating the Virial Coefficients
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.
Keywords
Cite
@article{arxiv.0907.4906,
title = {Inductive Construction of 2-Connected Graphs for Calculating the Virial Coefficients},
author = {E. Androulaki and S. Lambropoulou and I. G. Economou and J. H. Przytycki},
journal= {arXiv preprint arXiv:0907.4906},
year = {2015}
}
Comments
23 pages, 5 figures, 3 tables