Convert graph into ideal in polynomial ring
Let G=(V(G),E(G)) denote a finite simple (no loops or multiple edges) undirected graph with vertices V(G)= x1,…,xn and edge set E(G) . By identifying the vertices with the variables in the polynomial ring R=k[x1,…,xn] (where k is a field), we can associate to each simple graph G a monomial ideal I(G)=(xixj|xi,xj∈E(G))
How to convert graph into ideal in sage ? Suppose G is cycle graph. can i get ideal with generator (x1x2,x2x3,x3x4,x4x5,x1x5) in k[x1,…,x5] Please give some hint.
Thanks in advance