Ne isotopes measured in individual presolar graphite grains, solid samples of extinct stars preserved in primitive meteorites, provide information on the type of stellar sources of the grains and on nucleosynthetic mixing and ion-trapping processes which were operating. We present Ne and He isotope analyses of single presolar graphite grains from the KFB1 density fraction extracted from the carbonaceous chondrite Murchison. In addition, we measured isotopes of C, O, and Mg-Al with the NanoSIMS ion microprobe to better constrain the origin of the grains. Eleven out of 51 presolar graphite grains contain nucleosynthetic 22 Ne above our detection limit. This fraction of 22 Ne-rich grains is similar to the one reported by Nichols et al. although we have a lower 22 Ne detection limit. We detected rare He-shell 20 Ne in one 22 Ne-rich grain and obtained the 20 Ne/ 22 Ne ratio (0.03 ± 0.02) of the He-shell of an Asymptotic Giant Branch (AGB) star with 1.5-2 M and subsolar metallicity. We also detected 4 He in this grain, while in the other grains, which originally acquired He, He-loss seems to be significant. We found unequivocal evidence for radiogenic 22 Ne (Ne-R) in another graphite grain, which likely condensed in a core-collapse supernova and which incorporated live radioactive 22 Na (t 1/2 = 2.6 yr). For the other grains, a clear assignment to a stellar source is more difficult to make. Putative stellar sources are supernovae, AGB stars, born-again AGB stars, J-type carbon stars, and CO novae.