2 problems

Let $C_n$ be a cycle on $n$ vertices, let $W(C_n)$ denote its whiskered cycle, and let $I(G)$ be the edge ideal of a finite simple graph $G$. For $q\geq 1$, let $I(G)^{[q]}$ be the…

Let $W(C_m)$ be the graph obtained by attaching a whisker to each vertex of the cycle $C_m$, let $I(W(C_m))$ be its edge ideal in the corresponding polynomial ring…