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graffiti: graffiti: [19] Although it denotes ‘writing’, graffiti has no etymological connection with Greek gráphein, source of English graphic. It comes from the plural of Italian graffito, a diminutive form of the noun graffio ‘scratching’. This was derived from the verb graffiare ‘scratch’, itself originally formed from graffio ‘hook’.
graft: graft: [15] Graft, in its original sense ‘plant part inserted into a living plant’ (the application to skin and other animal tissue is a late 19thcentury development), came from its resemblance in shape to a pencil. Greek graphíon meant ‘writing implement, stylus’ (it was a derivative of the verb gráphein ‘write’, source of English graphic). It passed via Latin graphium into Old French as grafe, gradually changing in its precise application with the advance of writing technology.

By the time it reached Old French it denoted a ‘pencil’, and it was then that the resemblance to two artificially united plant stems was noted and the metaphor born. English took the word over as graff in the late 14th century (it actually survived in that form into the 19th century), and within a hundred years had added a -t to the end to give modern English graft. Graft ‘corruption’, first recorded in mid 19th-century America, may be the same word, perhaps derived from the notion of a graft as an ‘insertion’, hence ‘something extra, on the side’. Graft ‘hard work’ [19], on the other hand, is probably a different word, perhaps based on the English dialect verb graft ‘dig’, an alteration of grave ‘dig’.
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engraft (v.): 1580s, from en- (1) + graft (n.). Originally figurative. Related: Engrafted; engrafting.
graffiti (n.): 1851, "ancient wall inscriptions found in the ruins of Pompeii," from Italian graffiti, plural of graffito "a scribbling," a diminutive formation from graffio "a scratch or scribble," from graffiare "to scribble," ultimately from Greek graphein "to scratch, draw, write" (see -graphy). They are found in many ancient places, but the habit was especially popular among the Romans. Sense extended 1877 to recently made crude drawings and scribbling in public places.
graffito (n.): singular of graffiti (q.v.).
graft (n.1): "shoot inserted into another plant," late 15c. alteration of Middle English graff (late 14c.), from Old French graife "grafting knife, carving tool; stylus, pen," from Latin graphium "stylus," from Greek grapheion "stylus," from graphein "to write" (see -graphy). So called probably on resemblance of a stylus to the pencil-shaped shoots used in grafting. The terminal -t- in the English word is not explained. Surgical sense is from 1871.
graft (n.2): "corruption," 1865, perhaps 1859, American English, perhaps from British slang graft "one's occupation" (1853), which is perhaps from the identical word meaning "a ditch, moat," literally "a digging" (1640s), from Middle Dutch graft, from graven "to dig" (see grave (v.)).
graft (v.): late 15c., "insert a shoot from one tree into another," from graft (n.1). Figurative use by 1530s. Surgical sense by 1868. Related: Grafted; grafting.