On graphs without a C4 or a diamond

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. [email protected], Lane Department of Computer Science and Electrical Engineering, P.O. Box 6109, West Virginia University, Morgantown, WV 26506. [email protected], Department of Physics and Computing, Wilfrid Laurier University, Waterloo, Canada. Acknowledges support from NSERC of Canada. [email protected], Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN 37235. [email protected], Computer Science Department, The University of Dayton, Dayton, OH 45469. Acknowledges support from the National Security Agency.