On colour-preserving automorphisms of Cayley graphs
Ademir Hujdurovi\'c, Klavdija Kutnar, Dave Witte Morris, and Joy, Morris

TL;DR
This paper investigates the structure of automorphisms of Cayley graphs that preserve or permute edge colours, identifying groups with simple automorphism forms and classifying groups lacking this property.
Contribution
It characterizes groups for which all colour-preserving automorphisms of Cayley graphs are composed of left-translations and automorphisms, and classifies groups without this property.
Findings
Identified classes of groups with simple automorphism structures
Determined orders of groups lacking the property
Extended results to colour-permuting automorphisms
Abstract
We study the automorphisms of a Cayley graph that preserve its natural edge-colouring. More precisely, we are interested in groups G, such that every such automorphism of every connected Cayley graph on G has a very simple form: the composition of a left-translation and a group automorphism. We find classes of groups that have the property, and we determine the orders of all groups that do not have the property. We also have analogous results for automorphisms that permute the colours, rather than preserving them.
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Taxonomy
TopicsFinite Group Theory Research · graph theory and CDMA systems · Coding theory and cryptography
