On graphs without multicliqual edges - Lim, Chong Keang; Peng, Yee Hock (John Wiley & Sons, 1981)
An edge which belongs to more than one clique of a given graph is called a multicliqual edge. We find a necessary and sufficient condition for a graph H to be the clique graph of some graph G without multicliqual edges. We also give a characterization of graphs without multicliqual edges that have a unique critical generator. Finally, it is shown that there are infinitely many self-clique graphs having more than one critical generator.