In our study of carbon vapor molecules trapped in Ne matrices at 6 K, we observed laser induced fluorescence spectra of the D (1)Sigma(u)(+)-->B-' (1)Sigma(g)(+) system of C-2 upon excitation of the Mulliken transition D (1)Sigma(u)(+)<--X (1)Sigma(g)(+) of C-2 at 232 nm. A vibrational progression was clearly observed going from the upper vibrational v(')=0 level of the electronic D state into several lower v(')=0-6 levels of the B-' state. We found that the progression spans from 359 to 517 nm with a large Franck-Condon shift showing the intensity maximum for the 0-2 or 0-3 transition. The vibrational constants for the B-' state were derived as omega(e)=1427 cm-1 and omega(e)x(e)=2.1 cm(-1). We also observed the C-->A and the Swan band emissions, showing that from the excited D state also additional states were populated by internal conversion and intersystem crossing. The constants for the A state were derived as omega(e)=1613.5 cm(-1) and omega(e)x(e)=18.5 cm(-1). Fluorescence excitation spectra of the D-->B-' vibronic transitions were found to reproduce well the relatively narrow absorption feature of the Mulliken D<--X system. We discuss the entirely different excitation spectra occurring in argon matrices in terms of matrix-site effects. Each vibronic band of the D-->B-' progression shows fine structures probably due to translations and librations of C-2 molecules coupled with the surrounding lattice of Ne atoms.