The Smith normal form of distance matrices of high dimensional trees

Carlos A. Alfaro, Jesús Uriel Medrano, Iván Téllez Téllez

Graham-Lovász-Pollak \cite{GL,GP} obtained the celebrated formula $$\det (\mathsf{D}(T_{n+1}))=(-1{)}^{n}n{2}^{n-1},$$ for the determinant of the distance matrix $\mathsf{D}(T_{n+1})$ for any t…