Morris, Joy

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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.
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