2 problems

Let $G=(V,E)$ be a finite bipartite graph. For $x\in(-1,1)$, let $\tau(G,x)=\det(\Sigma(G,x))$, where $\Sigma(G,x)$ is the unique positive-definite matrix with diagonal entries $1$…

Let $G=(V,E)$ be a finite graph. For $x otin(-1,1)$? [sic] the paper defines $\tau(G,x)=\det(\Sigma(G,x))$, where $\Sigma(G,x)$ is the unique positive-definite matrix with diagonal ent…