Normal Polytopes Arising from Finite Graphs

Abstract Let G be a finite connected graph on the vertex set {1,…, d } allowing loops and having no multiple edge. Let K [ t 1 ,…, t d ] denote the polynomial ring in d indeterminates over a field K and let K [ G ] be the subalgebra of K [ t 1 ,…, t d ] generated by all quadratic monomials t i t j such that { i ,  j } is an edge of G and by all quadratic monomials t 2 i such that G has a loop at i . We describe the normalization of K [ G ] explicitly and we give a combinatorial criterion for K [ G ] to be normal.