Report Number: CS-TR-72-273
Institution: Stanford University, Department of Computer Science
Title: Chromatic automorphisms of graphs.
Author: Chvatal, Vaclav
Author: Sichler, Jiri
Date: March 1972
Abstract: The coloring group and the full automorphism group of an n-chromatic graph are independent if and only if n is an integer $\geq$ 3.
http://i.stanford.edu/pub/cstr/reports/cs/tr/72/273/CS-TR-72-273.pdf