Fragments of C24H12, adapted from a variety of armchair [(n,n), (n = 5, 7, and 8)] and zigzag [(m,0) (m = 8, 10, and 12)] single-walled carbon nanotube (SWCNT), are used to model corresponding SWCNTs with different diameters and electronic structures. The parallel binding mainly through pi...pi stacking interaction, as well as the perpendicular binding via cooperative NH...pi and CH...pi between cytosine and the fragments of SWCNT have been extensively investigated with a GGA type of DFT, PW91LYP/6-311++G(d,p). The eclipsed tangential (ET) conformation with respect to the six-membered ring of cytosine and the central ring of SWCNT fragments is less stable than the slipped tangential (ST) conformation for the given fragment; perpendicular conformations with NH2 and CH ends have higher negative binding energy than those with NH and CH ends. At PW91LYP/6-311++G(d,p) level, two tangential complexes are less bound than perpendicular complexes. However, as electron correlation is treated with MP2/6-311G(d,p) for PW91LYP/6-311++G(d,p) optimized complexes, it turns out there is an opposite trend that two tangential complexes become more stable than three perpendicular complexes. This result implies that electron correlation, a primary source to dispersion energy, has more significant contributions to the pi...pi stacking complexes than to the complexes via cooperative NH...pi and CH...pi interactions. In addition, it was found for the first time that binding energies for two tangential complexes become more negative with increasing nanotube diameter, while those for three perpendicular complexes have a weaker dependence on the curvature; i.e., binding energies are slightly less and less negative. The performance of a novel hybrid DFT, MPWB1K, was also discussed.