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

Androulaki, E; Lambropoulou, S; Economou, IG; Przytycki, JH

dc.contributor.author	Androulaki, E	en
dc.contributor.author	Lambropoulou, S	en
dc.contributor.author	Economou, IG	en
dc.contributor.author	Przytycki, JH	en
dc.date.accessioned	2014-03-01T02:00:25Z
dc.date.available	2014-03-01T02:00:25Z
dc.date.issued	2010	en
dc.identifier.issn	1751-8113	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29100
dc.subject.classification	Physics, Multidisciplinary	en
dc.subject.classification	Physics, Mathematical	en
dc.title	Inductive construction of 2-connected graphs for calculating the virial coefficients	en
heal.type	journalArticle	en
heal.identifier.secondary	315004	en
heal.language	English	en
heal.publicationDate	2010	en
heal.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.	en
heal.publisher	IOP PUBLISHING LTD	en
heal.journalName	JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL	en
dc.identifier.isi	ISI:000279874800006	en
dc.identifier.volume	43	en
dc.identifier.issue	31	en