  We classify generalized block graphs whose binomial edge ideals admit a
unique extremal Betti number. We prove that the Castelnuovo-Mumford regularity
of binomial edge ideals of generalized block graphs is bounded below by
$m(G)+1$, where $m(G)$ is the number of minimal cut sets of the graph $G$ and
obtain an improved upper bound for the regularity in terms of the number of
maximal cliques and pendant vertices of $G$.
