  A graph is said to be distance-hereditary if the distance function in every
connected induced subgraph is the same as in the graph itself. We prove that
the ordinary Weisfeiler-Leman algorithm correctly tests the isomorphism of any
two graphs if one of them is distance-hereditary; more precisely, the
Weisfeiler-Leman dimension of the class of finite distance-hereditary graphs is
equal to $2$. The previously best known upper bound for the dimension was $7$.

Combinatorics;Computational Complexity;Discrete Mathematics