On graphs without a image or a diamond Original Research Article

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