Some graph theoretical characterizations of positive definite symmetric   quasi-Cartan matrices
  We present some graphical characterizations of positive definite symmetric quasi-Cartan matrices of Dynkin type $\mathbb{A}_{n}$ and $\mathbb{D}_{n}$. Our proofs are constructive, purely graph theoretical, and almost self-contained in the sense that they rely on the classical inflations method only. 
M. Abarca and D. Rivera
math.CO