Inductive construction of 2-connected graphs for calculating the virial coefficients

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 o...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2010-08, Vol.43 (31), p.315004-315004
Main Authors: Androulaki, E, Lambropoulou, S, Economou, I G, Przytycki, J H
Format: Article
Language:English
Subjects:
Clusters
Construction
Equations of state
Exact sciences and technology
Graphs
Mathematical analysis
Physics
Statistical mechanics
Subdivisions
Virial coefficients
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Summary: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.
ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/43/31/315004