Simple Polytopes Arising From Finite Graphs
نویسندگان
چکیده
Let G be a finite graph allowing loops, having no multiple edge and no isolated vertex. We associate G with the edge polytope PG and the toric ideal IG. By classifying graphs whose edge polytope is simple, it is proved that the toric ideals IG of G possesses a quadratic Gröbner basis if the edge polytope PG 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.
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