Tutte polynomial and G-parking functions

Chang, HungYung; Ma, Jun; Yeh, Yeong-Nan

Tutte polynomial and G-parking functions

Authors

Chang, HungYung

Ma, Jun

Yeh, Yeong-Nan

Description

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.