On the number of clusters for planar graphs

Details On the number of clusters for planar graphs On the number of clusters for planar graphs

2006-06-19

arxiv.org/abs/cond-mat/0606495v1

Physics

Condensed Matter

Statistical Mechanics

14 pages

Scientific paper

The Tutte polynomial is a powerfull analytic tool to study the structure of planar graphs. In this paper, we establish some relations between the number of clusters per bond for planar graph and its dual : these relations bring into play the coordination number of the graphs. The factorial moment measure of the number of clusters per bond are given using the derivative of the Tutte polynomial. Examples are presented for simple planar graph. The cases of square, triangular, honeycomb, Archimedean and Laves lattices are discussed.

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