Geodesic
Graph Weights Arising From Mayer's Theory of Cluster Integrals
Séminaire lotharingien de combinatoire, Tome 54 (2006-2007) Cet article a éte moissonné depuis la source Séminaire Lotharingien de Combinatoire website

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We study graph weights (i.e., graph invariants) which arise naturally in Mayer's theory of cluster integrals in the context of a non-ideal gas. Various choices of the interaction potential between two particles yield various graph weights w(g). For example, in the case of the Gaussian interaction, the so-called Second Mayer weight w(c) of a connected graph c is closely related to the graph complexity, i.e., the number of spanning trees, of c. We give special attention to the Second Mayer weight w(c) which arises from the hard-core continuum gas in one dimension. This weight is a signed volume of a convex polytope P(c) naturally associated with c. Among our results are the values w(c) for all 2-connected graphs c of size at most 6, in Appendix B, and explicit formulas for three infinite families: complete graphs, (unoriented) cycles and complete graphs minus an edge. 

@article{SLC_2006-2007_54_a12,
     author = {Gilbert Labelle and Pierre Leroux and Martin G. Ducharme},
     title = {Graph {Weights} {Arising} {From} {Mayer's} {Theory} of {Cluster} {Integrals}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2006-2007},
     volume = {54},
     url = {http://geodesic.mathdoc.fr/item/SLC_2006-2007_54_a12/}
}
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AU  - Pierre Leroux
AU  - Martin G. Ducharme
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Gilbert Labelle; Pierre Leroux; Martin G. Ducharme. Graph Weights Arising From Mayer's Theory of Cluster Integrals. Séminaire lotharingien de combinatoire, Tome 54 (2006-2007). http://geodesic.mathdoc.fr/item/SLC_2006-2007_54_a12/