Morris, Joy

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https://opus.uleth.ca/handle/10133/4941

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Browsing Morris, Joy by Subject "Colour preserving"

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    Two new families of non-CCA groups
    (University of Primorska, 2021) Fuller, Brandon; Morris, Joy
    We determine two new infinite families of Cayley graphs that admit colour-preserving automorphisms that do not come from the group action. By definition, this means that these Cayley graphs fail to have the CCA (Cayley Colour Automorphism) property, and the corresponding infinite families of groups also fail to have the CCA property. The families of groups consist of the direct product of any dihedral group of order 2n where n ≥ 3 is odd, with either itself, or the cyclic group of order n. In particular, this family of examples includes the smallest non-CCA group that does not fit into any previous family of known non-CCA groups.
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    Vertex-transitive digraphs with extra automorphisms that preserve the natural arc-colouring
    (The University of Queensland, Centre for Discrete Mathematics and Computing, 2017) Dobson, Ted; Hujdurovic, Ademir; Kutnar, Klavdija; Morris, Joy
    In a Cayley digraph on a group G, if a distinct colour is assigned to each arc-orbit under the left-regular action of G, it is not hard to show that the elements of the left-regular action of G are the only digraph automorphisms that preserve this colouring. In this paper, we show that the equivalent statement is not true in the most straightforward generalisation to G-vertex-transitive digraphs, even if we restrict the situation to avoid some obvious potential problems. Specifically, we display an infinite family of 2-closed groups G, and a G-arc-transitive digraph on each (without any digons) for which there exists an automorphism of the digraph that is not an element of G (it is an automorphism of G). Since the digraph is G-arc-transitive, the arcs would all be assigned the same colour under the colouring by arc-orbits, so this digraph automorphism is colour-preserving.