8,964 research outputs found
Strongly regular edge-transitive graphs
In this paper, we examine the structure of vertex- and edge-transitive
strongly regular graphs, using normal quotient reduction. We show that the
irreducible graphs in this family have quasiprimitive 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.Comment: 23 page
Relative Quasiconvexity using Fine Hyperbolic Graphs
We provide a new and elegant approach to relative quasiconvexity for
relatively hyperbolic groups in the context of Bowditch's approach to relative
hyperbolicity using cocompact actions on fine hyperbolic graphs. Our approach
to quasiconvexity generalizes the other definitions in the literature that
apply only for countable relatively hyperbolic groups. We also provide an
elementary and self-contained proof that relatively quasiconvex subgroups are
relatively hyperbolic.Comment: 21 pages, 6 figures. New section on fine graphs. Version to appear in
AG
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