Distance matrices of partial cubes

Partial cubes are isometric subgraphs of hypercubes. Median graph is a graph in which every three vertices u,v and w have a unique median: a vertex m that belongs to shortest paths between each pair of u,v and w. Median graphs present one of the most studied subclasses of partial cubes. We determine the Smith normal form of the distance matrices of partial cubes and the factorisation of Varchenko determinant of product distance matrices of median graphs.