  Given a positive-weighted simple connected graph with $m$ vertices, labelled
by the numbers $1,\ldots,m$, we can construct an $m \times m$ matrix whose
entry $(i,j)$, for any $i,j\in\{1,\dots,m\}$, is the minimal weight of a path
between $i$ and $j$, where the weight of a path is the sum of the weights of
its edges. Such a matrix is called the distance matrix of the weighted graph.
There is wide literature about distance matrices of weighted graphs. In this
paper we characterize distance matrices of positive-weighted $n$-hypercube
graphs. Moreover we show that a connected bipartite $n$-regular graph with
order $2^n$ is not necessarily the $n$-hypercube graph. Finally we give a
characterization of distance matrices of positive-weighted Petersen graphs.
