On graphs without a or a diamond

Abstract: We consider the class of (, diamond)-free graphs; graphs in this class do not contain a 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 (, diamond)-free graph and the number of -vertex, labeled (, diamond)-free graphs. We also give an efficient algorithm for finding a largest clique in the more general class of (house, diamond)-free graphs. [Copyright &y& Elsevier]