Inductive construction of 2-connected graphs for calculating the virial coefficients
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© 2010 IOP Publishing Ltd. 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 labeled 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.
author list (cited authors)
Androulaki, E., Lambropoulou, S., Economou, I. G., & Przytycki, J. H.