The　traditional　classical　fullerene　is　only　composed　of　pentagons　and　hexagons,　with　many　different　topologies,　of　which　only　a　few　structures　conform　to　the　isolated　pentagon　rule　(IPR),　which　means　all　five-membered　rings　are　separated　by　hexagons,　whereas　isomers　that　violate　the　rule　are　called　non-IPR　isomers.　In　contrast,　the　non-classical　fullerene　consists　of　other　kinds　of　polygons　such　as　squares　and　heptagons　in　addition　to　pentagons　and　hexagons.　X-ray　photoelectron　spectra　(XPS),　near-edge　X-ray　absorption　fine　structure　(NEXAFS)　spectra　and　X-ray　emission　spectra　(XES),　as　well　as　the　ground-state　electronic/geometrical　structures　of　the　important　non-IPR　isomers　C3v-#1205C58　and　C2-#1078C58,　and　the　remarkable　non-classical　isomer　Cs-C58(NC)　with　its　two　fluorides　Cs-C58(NC)F18(A)　and　Cs-C58(NC)F18(B),　have　been　computed　at　the　density　functional　theory　(DFT)　level.　Significant　differences　in　the　electronic　structures　and　simulated　X-ray　spectra　have　been　observed　after　fluorination.　Meanwhile,　strong　isomer　dependence　has　been　shown　in　these　spectra,　which　means　the　＇fingerprint＇in　the　X-ray　spectra　can　effectively　identify　the　above-mentioned　fullerene　isomers.　As　a　consequence,　the　work　can　provide　useful　information　especially　isomer　identification　for　experimental　and　theoretical　research　in　fullerene　science.　©　The　Royal　Society　of　Chemistry.