Morris, Joy; Praeger, Cheryl E.; Spiga, Pablo(Drustvo Matematikov, Fizikov in AstronomovArts and ScienceDepartment of Mathematics and Computer ScienceUniversity of LethbridgeUniversity of Western AustraliaUniversity of Padova, 2009)
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, ...
Kutnar, Klavdija; Marusic, Dragan; Morris, Dave Witte; Morris, Joy; Sparl, Primoz(Drustvo Matematikov, Fizikov in AstronomovArts and ScienceDepartment of Mathematics and Computer ScienceUniversity of PrimorskaUniversity of LjubljanaUniversity of Lethbridge, 2012)
We prove that if Cay(G;S) is a connected Cayley graph with n vertices,and the prime factorization of n is very small, then Cay(G;S) has a hamiltonian cycle. More precisely, if p, q, and r are distinct primes, then n can ...
Bhoumik, Soumya; Dobson, Edward; Morris, Joy(Drustvo Matematikov, Fizikov in AstronomovArts and ScienceDepartment of Mathematics and Computer ScienceFort Hays State UniversityMississippi State UniversityUniversity of PrimorskaUniversity of Lethbridge, 2018)
We attempt to determine the structure of the automorphism group of a generic circulant graph. We ﬁrst show that almost all circulant graphs have automorphism groups as small as possible. The second author has conjectured ...
Hujdurovic, Ademir; Kutnar, Klavdija; Morris, Dave Witte; Morris, Joy(Drustvo Matematikov, Fizikov in AstronomovArts and ScienceDepartment of Mathematics and Computer ScienceUniversity of PrimorskaUniversity of Lethbridge, 2016)
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 ...
Morris, Joy(University of Calgary, Department of Mathematics & StatisticsArts and ScienceDepartment of Mathematics and Computer ScienceUniversity of Lethbridge, 2016)
In this paper, we begin by partitioning the edge (or arc) set of a circulant (di)graph according to which generator in the connection set leads to each edge. We then further reﬁne the partition by subdividing any part that ...
Curran, Stephen J.; Morris, Dave Witte; Morris, Joy(Drustvo Matematikov, Fizikov in AstronomovArts and ScienceDepartment of Mathematics and Computer ScienceUniversity of Pittsburgh at JohnstownUniversity of Lethbridge, 2012)
Suppose G is a ﬁnite group, such that |G| = 16p, where p is prime. We show that if S is any generating set of G, then there is a hamiltonian cycle in the corresponding Cayley graph Cay(G;S).
Morgan, Luke; Morris, Joy; Verret, Gabriel(Drustvo Matematikov, Fizikov in AstronomovArts and ScienceDepartment of Mathematics and Computer ScienceUniversity of Western AustraliaUniversity of Lethbridge, 2018)
A Cayley graph on a group G has a natural edge-colouring. We say that such a graph is CCA if every automorphism of the graph that preserves this edge-colouring is an element of the normaliser of the regular representation ...
Dobson, Ted; Hujdurovic, Ademir; Kutnar, Klavdija; Morris, Joy(The University of Queensland, Centre for Discrete Mathematics and ComputingArts and ScienceDepartment of Mathematics and Computer ScienceMississippi State UniversityUniversity of PrimoskaUniversity of Lethbridge, 2017)
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 ...
Dobson, Edward; Morris, Joy(Electronic Journal of CombinatoricsArts and ScienceDepartment of Mathematics and Computer ScienceMississippi State UniversityUniversity of Lethbridge, 2002)
Let S be a subset of the units in Zn. Let Γ be a circulant graph of order n (a Cayley graph of Zn) such that if ij ∈ E(Γ), then i − j (mod n) ∈ S. Toida conjectured that if Γ0 is another circulant graph of order n, then Γ ...
Dobson, Edward; Morris, Joy(Electronic Journal of CombinatoricsArts and ScienceDepartment of Mathematics and Computer ScienceMississippi State UniversityUniversity of Lethbridge, 2009)
We generalize a classical result of Sabidussi that was improved by Hemminger, to the case of directed color graphs. The original results give a necessary and suﬃcient condition on two graphs, C and D, for the automorphsim ...
Jordan, Heather; Morris, Joy(The University of Queensland, Centre for Discrete Mathematics and ComputingArts and ScienceDepartment of Mathematics and Computer ScienceAlbion CollegeUniversity of Lethbridge, 2017)
In this paper, we provide necessary and suﬃcient conditions for the existence of a cyclic m-cycle system of Kn −I when m and n are even and m | n.
Morris, Joy(Electronic Journal of CombinatoricsArts and ScienceDepartment of Mathematics and Computer ScienceUniversity of Lethbridge, 2016)
A ﬁnite group G is a DCI-group if, whenever S and S0 are subsets of G with the Cayley graphs Cay(G,S) and Cay(G,S0) isomorphic, there exists an automorphism ϕ of G with ϕ(S) = S0. It is a CI-group if this condition holds ...
Morris, Joy; Spiga, Pablo; Verret, Gabriel(Electronic Journal of CombinatoricsArts and ScienceDepartment of Mathematics and Computer ScienceUniversity of LethbridgeUniversity of Milano-BicoccaThe University of Western Australia, 2015)
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 ...