Friday, October 28, 2011
Hall 1-2 (San Jose Convention Center)
We find an infinite family of directed strongly regular graphs whose automorphism groups
are vertex-transitive. We explore a subfamily of the above family, that has a transitive
action rank equal to six. Thus, the 2-orbits (or orbitals) of the vertex-transitive permutation
group form a non-commutative association scheme of class 5. We describe the construction
of the graphs, calculation of automorphisms, and show the transitivity. We then discuss
the relationships between the directed strongly regular graph, the association scheme
obtained from the permutation, and the strongly regular graphs obtained from a fusion of
the association scheme as time permits.
are vertex-transitive. We explore a subfamily of the above family, that has a transitive
action rank equal to six. Thus, the 2-orbits (or orbitals) of the vertex-transitive permutation
group form a non-commutative association scheme of class 5. We describe the construction
of the graphs, calculation of automorphisms, and show the transitivity. We then discuss
the relationships between the directed strongly regular graph, the association scheme
obtained from the permutation, and the strongly regular graphs obtained from a fusion of
the association scheme as time permits.