16 citations · 77 across the 45 of their papers we have counts for
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Arc-transitive digraphs with quasiprimitive local actions
Michael Giudici, S. P. Glasby, Cai Heng Li +1
Let be a finite -vertex-transitive digraph. The in-local action of is the permutation group induced by the vertex-stabiliser on the set of in-neighbours of …
Primitive permutation groups with a suborbit of length 5 and vertex-primitive graphs of valency 5
Joanna B. Fawcett, Michael Giudici, Cai Heng Li +3
We classify finite primitive permutation groups having a suborbit of length 5. As a corollary, we obtain a classification of finite vertex-primitive graphs of valency 5. In the pro…
Isomorphisms of Cayley graphs on nilpotent groups
Dave Witte Morris, Joy Morris, Gabriel Verret
Let S be a finite generating set of a torsion-free, nilpotent group G. We show that every automorphism of the Cayley graph Cay(G;S) is affine. (That is, every automorphism of the g…
Cubic arc-transitive -circulants
Michael Giudici, István Kovács, Cai Heng Li +1
For an integer , a graph is called a -circulant if its automorphism group contains a cyclic semiregular subgroup with orbits on the vertices. We show that, if i…
The number of composition factors of order in completely reducible groups of characteristic
Michael Giudici, S. P. Glasby, Cai Heng Li +1
Let be a power of a prime and let be a completely reducible subgroup of . We prove that the number of composition factors of that have prime order…