Quantum walks do not like bridges

We consider graphs with two cut vertices joined by a path one or edges, and prove that there can be no quantum perfect state transfer between these vertices, unless the graph has other vertex. achieve this result applying 1-sum lemma for characteristic polynomial of graphs, neutrino identities relate entries eigenprojectors eigenvalues, variational principles eigenvalues (Cauchy interlacing theorem, Weyl inequalities Wielandt minimax principle). see our as an intermediate step to broaden understanding how connectivity plays key role in walks, further evidence conjecture tree on four more admits transfer. conclude some open problems.