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Tutte polynomial and G-parking functions | | HungYung Chang
; Jun Ma
; Yeong-Nan Yeh
; | | Date: |
15 Dec 2008 | | Abstract: | Let $G$ be a connected graph with vertex set ${0,1,2,...,n}$. We allow $G$
to have multiple edges and loops. In this paper, we give a characterization of
external activity by some parameters of $G$-parking functions. In particular,
we give the definition of the bridge vertex of a $G$-parking function and
obtain an expression of the Tutte polynomial $T_G(x,y)$ of $G$ in terms of
$G$-parking functions. We find the Tutte polynomial enumerates the $G$-parking
function by the number of the bridge vertices. | | Source: | arXiv, 0812.2817 | | Services: | Forum | Review | PDF | Favorites | |
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