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Using the concept of prime graphs and modular decomposition of graphs, we give a complete structure description of (P5,diamond)-free graphs implying that these graphs have bounded clique width (the P5 is the induced path with ÿve vertices a; b; c; d; e and four edges ab; bc; cd; de, and the diamond consists of four vertices a; b; c; d such that a; b; c form an induced path with edges ab; bc, and vertex d is adjacent to a; b and c). The structure and bounded clique width of this graph classdoi:10.1016/s0166-218x(03)00266-x fatcat:54ihrkjzlnc3holpwtjzzcyy54