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We performed resonant Raman/fluorescence spectroscopic studies on double-walled carbon nanotubes (DWNTs) that were dispersed in an aqueous single stranded DNA solution. The luminescence signals from the inner tubes of DWNTs are intensified in the isolated state of each individual DWNT. The completely depressed radial breathing modes (RBMs) associated with the outer tubes (whether semiconducting or metallic) via the mechanical wrapping and the strong charge transfer between DNA and the outer tubes support our interpretation that the bright luminescence and sharp absorption spectra come from only the inner tubes, and not from isolated SWNTs. The circumferentially wrapped DNA on the outer tubes of individually isolated DWNTs in an aqueous solution gives rise to strong charge transfer to the semiconducting and metallic outer tubes as well as to generating physical strain in the outer tubes.