2 problems

Let $G$ be a graph on the vertex set $x,y$ with adjacency matrix … Assume $A\geq D$, $A,B,C,D>0$, and $(A-C)(B-D)<0$, and let $\mathcal{M}(G)$ denote its graph monoid. Graph-monoid…

Let $E$ be a row-finite directed graph, let $M_E^\Gamma$ be its cancellative commutative monoid with a $\Gamma$-action, and let $G_E^\Gamma$ be its Grothendieck group, equipped wit…