Several extreme coefficients of the Tutte polynomial of graphs

Helin Gong, Mengchen Li, Xian'an Jin

Let $t_{i,j}$ be the coefficient of $x^i{y}^j$ in the Tutte polynomial $T(G;x,y)$ of a connected bridgeless and loopless graph $G$ with order $n$ and size $m$. It is trivial that $t_…