  A cluster graph is a graph whose every connected component is a complete
graph. Given a simple undirected graph $G$, a subset of vertices inducing a
cluster graph is called an independent union of cliques (IUC), and the IUC
polytope associated with $G$ is defined as the convex hull of the incidence
vectors of all IUCs in the graph. The {\sc Maximum IUC} problem, which is to
find a maximum-cardinality IUC in a graph, finds applications in network-based
data analysis. In this paper, we derive several families of facet-defining
valid inequalities for the IUC polytope. We also give a complete description of
this polytope for some special classes of graphs. We establish computational
complexity of the separation problem for most of the considered families of
valid inequalities and explore the effectiveness of employing the corresponding
cutting planes in an integer (linear) programming framework for the {\sc
Maximum IUC} problem through computational experiments.
