Morris, Joy

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

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Browsing Morris, Joy by Author "Spiga, Pablo"

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    Groups with elements of order 8 do not have the DCI property
    (University of Primorska, 2025) Dobson, Ted; Morris, Joy; Spiga, Pablo
    Let k be odd, and n an odd multiple of 3. Although this can also be deduced from known results, we provide a new proof that Ck ⋊ C₈ and (Cn × C₃) ⋊ C₈ do not have the Directed Cayley Isomorphism (DCI) property. When k is prime, Ck ⋊ C₈ had previously been proved to have the Cayley Isomorphism (CI) property. To the best of our knowledge, the groups Cp ⋊ C₈ (where p is an odd prime) are only the second known infinite family of groups that have the CI property but do not have the DCI property. This also provides a new proof of the result (which follows from known results but was not explicitly published) that no group with an element of order 8 has the DCI property. One piece of our proof is a new result that may prove to be of independent interest: we show that if a permutation group has a regular subgroup of index 2 then it must be 2-closed.
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    Haar graphical representations of finite groups and an application to poset representations
    (Elsevier, 2025) Morris, Joy; Spiga, Pablo
    Answering a question of Feng, Kovács, Wang, and Yang, we classify the finite groups admitting a Haar graphical representation. Specifically, we show that every finite group admits a Haar graphical representation, with abelian groups and ten other small groups as the only exceptions. Our work on Haar graphs allows us to improve a 1980 result of Babai concerning representations of groups on posets, achieving the best possible result in this direction. An improvement to Babai's related result on representations of groups on distributive lattices follows.
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    On the asymptotic enumeration of Cayley graphs
    (Springer, 2021) Morris, Joy; Moscatiello, Mariapia; Spiga, Pablo
    In this paper, we are interested in the asymptotic enumeration of Cayley graphs. It has previously been shown that almost every Cayley digraph has the smallest possible auto- morphism group: that is, it is a digraphical regular representation (DRR). In this paper, we approach the corresponding question for undirected Cayley graphs. The situation is com- plicated by the fact that there are two infinite families of groups that do not admit any graphical regular representation (GRR). The strategy for digraphs involved analysing sepa- rately the cases where the regular group R has a nontrivial proper normal subgroup N with the property that the automorphism group of the digraph fixes each N-coset setwise, and the cases where it does not. In this paper, we deal with undirected graphs in the case where the regular group has such a nontrivial proper normal subgroup.
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    Semiregular automorphisms of cubic vertex-transitive graphs and the abelian normal quotient method
    (Electronic Journal of Combinatorics, 2015) Morris, Joy; Spiga, Pablo; Verret, Gabriel
    We characterise connected cubic graphs admitting a vertex-transitive group of automorphisms with an abelian normal subgroup that is not semiregular. We illustrate the utility of this result by using it to prove that the order of a semiregular subgroup of maximum order in a vertex-transitive group of automorphisms of a connected cubic graph grows with the order of the graph.
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    Strongly regular edge-transitive graphs
    (Drustvo Matematikov, Fizikov in Astronomov, 2009) Morris, Joy; Praeger, Cheryl E.; Spiga, Pablo
    In this paper, we examine the structure of vertex- and edge-transitive strongly regular graphs,using normal quotient reduction. We show that their reducible graphs in this family have quasi primitive automorphism groups, and prove (using the Classification of Finite Simple Groups) that no graph in this family has a holomorphic simple automorphism group. We also find some constraints on the parameters of the graphs in this family that reduce to complete graphs