  We consider the class of (C4, diamond)-free graphs; graphs in this class do
not contain a C4 or a diamond as an induced subgraph. We provide an efficient
recognition algorithm for this class. We count the number of maximal cliques in
a (C4, diamond)-free graph and the number of n-vertex, labeled (C4,
diamond)-free graphs. We also give an efficient algorithm for finding a largest
clique in the more general class of (house, diamond)-free graphs.
