  In extremal graph theory, the problem of finding the elements of a given
class of graphs which contain the most cliques traces its routes back to
Tur\'an's famous theorem. We consider the implications of the connectivity
property of simplicial complexes known as shellability on clique complexes
associated with graphs. In this paper, we find the graphs which maximize
cliques among all graphs on $n$ vertices with $\Delta(G)\leq r$ that have
shellable clique complexes.
