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We prove that every (claw, net)-free graph contains an induced doubly dominating cycle or a dominating pair. Moreover, using LexBFS we present a linear time algorithm which, for a given (claw, net)-free graph, ÿnds either a dominating pair or an induced doubly dominating cycle. We show also how one can use structural properties of (claw, net)-free graphs to solve e ciently the domination, independent domination, and independent set problems on these graphs. ?doi:10.1016/s0166-218x(02)00571-1 fatcat:2pbmjgfx7zfj7hwy3cz2djmtlm