Let $G = (V (G), E(G))$ denote a finite simple (no loops or multiple edges) undirected graph with vertices $V (G) =\ {x_1 ,\ldots, x_n }$ and edge set $E(G)$ . By identifying the vertices with the variables in the polynomial ring $R = k[x_1 ,\ldots, x_n ]$ (where $k$ is a field), we can associate to each simple graph $G$ a monomial ideal $I(G) = ({ x_i x_j |{x_i , x_j } \in E(G)})$
How to convert graph into ideal in sage ? Suppose $G$ is cycle graph. can i get ideal with generator $(x_1x_2,x_2x_3,x_3x_4,x_4x_5,x_1x_5)$ in $k[x_1,\ldots ,x_5]$ Please give some hint.