Green’s Dictionary of Slang

1. an alligator skin shoe; thus in pl., a pair of such shoes.

a.1986		‘Old Zebra Dun’ in G. Logsdon Whorehouse Bells Were Ringing (1995) 82: You could tell he was a feller not accustomed to the trail, / With his ’gators and his leggin’s and his fancy swaller tail.
1992		S.L. Hills Tragic Magic 29: I had six or seven pairs of gators.
2000		Eminem ‘Under the Influence’ 🎵 Accused for every crime known thru the equator / They knew I did it, for havin’ blood on my gators.
2006		G. Pelecanos Night Gardener 89: The man’s phony gators, which had been flaking off.
2011		G. Hayward Corruption Officer [ebk] cap. 11: He just buys mink coats and gator shoes.
2012		‘Dutch’ ? (Pronounced Que) [ebook] I do the gators from time to time.

2. (US campus, also alligator) a typical fraternity boy [the alligator emblem that is the trademark of Izod shirts, popular among fraternity wearers].

1981		Eble Campus Sl. Mar. 1: alligator – person who identifies with the fraternity/sorority way of life.
1996		Eble Sl. and Sociability 64: ‘A stereotypical fraternity member’ [...] was called a gator because of the alligator emblem on the once popular Izod shirts.