@article {
orvium-5ca50abe835e09000186f88e,
title = "Simple polytopes arising from finite graphs",
abstract = " Let $G$ be a finite graph allowing loops, having no multiple edge and no isolated vertex. We associate $G$ with the edge polytope ${\cal P}_G$ and the toric ideal $I_G$. By classifying graphs whose edge polytope is simple, it is proved that the toric ideals $I_G$ of $G$ possesses a quadratic Gr\"obner basis if the edge polytope ${\cal P}_G$ of $G$ is simple. It is also shown that, for a finite graph $G$, the edge polytope is simple but not a simplex if and only if it is smooth but not a simplex. Moreover, the Ehrhart polynomial and the normalized volume of simple edge polytopes are computed. Comment: 11 pages",
keywords = "",
author = " Hidefumi Ohsugi and Takayuki Hibi",
year = "2008",
language = "English",
url = "https://dapp.orvium.io/deposits/5ca50abe835e09000186f88e/view",
}