Two relations for median graphs

We generalize the well-known relation for trees n−m=1 to the class of median graphs in the following way. Denote by qi the number of subgraphs isomorphic to the hypercube Qi in a median graph. Then, ∑i⩾0 (−1)iqi=1. We also give an explicit formula for the number of Θ-classes in a median graph as k=−∑i⩾0 (−1)i iqi.