calligraffiti
n. Graffiti that uses or is inspired by calligraphic letterforms and techniques.
calligraffitist n.

Example Citations:
This, explains Shoe, is the fundamental idea behind what he describes as calligraffiti. The form of art he says he conceived in 2007, which as the name suggests, is a fusion of calligraphy and graffiti.
—Flavia Di Consiglio, “"Calligraffiti": The graffiti artist inspired by medieval scribes,“ BBC News, August 6, 2013

The artist"s assistant Khalid Ali explains that his style, known as calligraffiti, combines the raw improvisation of “tagging“ with the sweeping arabesques of traditional Islamic calligraphy.
—Mark Hudson, “Museum of Islamic Art in Doha: "It"s about creating an audience for art",“ The Telegraph, March 20, 2013

Earliest Citation:
The words were written in a hurried, unaccomplished new world hand, unlike the calligraffiti that honors the bricks of warehouses and the concrete of overpasses elsewhere in Europe, evidence that even in vandalism tradition is superiority.
—H. L. Hix, Spirits Hovering Over the Ashes, State University of New York Press, July 1, 1995

Notes:
It's possible this term is much older, since it appears in a photo caption from the May 1978 issue of The Unesco Courier:

Like a chick emerging from an egg this tiny Japanese girl climbs through a hole in a calligraffiti-covered wall at the Osaka World Exposition.
—Photo caption, The Unesco Courier (PDF), May 1, 1978
However, the wall in question, while certainly graffiti-covered, displays only a few Japanese characters, so there's no real calligraphy in sight, making this a most curious usage. The word also appeared in the name of various art shows and artworks in the 1980s and 90s.

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