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

E. Androulaki, S. Lambropoulou, Ioannis Economou, J. H. Przytycki

Research output: Contribution to journalArticle

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 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.

Original languageEnglish
Article number315004
JournalJournal of Physics A: Mathematical and Theoretical
Volume43
Issue number31
DOIs
Publication statusPublished - 6 Jul 2010
Externally publishedYes

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virial coefficients
Equations of state
Connected graph
apexes
Statistical mechanics
Coefficient
equations of state
Equation of State
subdivisions
Gases
statistical mechanics
induction
Graph in graph theory
Subdivision
Statistical Mechanics
Proof by induction
Correspondence
coefficients
gases
Vertex of a graph

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Inductive construction of 2-connected graphs for calculating the virial coefficients. / Androulaki, E.; Lambropoulou, S.; Economou, Ioannis; Przytycki, J. H.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 43, No. 31, 315004, 06.07.2010.

Research output: Contribution to journalArticle

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