2022/07/04 by Nayana Shibu Deepthi, Deepthi, Nayana Shibu
Mathematics · #Commutative Algebra and Its Applications #Graph theory and applications #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2207.01217
Let G be a finite simple connected graph on the vertex set V(G)=[d]=\1,… ,d\, with edge set E(G)=\e1,… , en\. Let K[t]=K[t1,… , td] be the polynomial ring in d variables over a field K. The edge ring of G is the semigroup ring K[G] generated by monomials te:=titj, for e=\i,j\ ∈ E(G). In this paper, we will prove that, given integers d and n, where d≥ 7 and d+1≤ n≤ \fracd2-7d+242, there exists a finite simple connected graph G with |V(G)|=d and |E(G)|=n, such that K[G] is non-normal and satisfies (S2)-condition.