A structure theorem for boundary-transitive graphs with infinitely many ends
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We prove a structure theorem for locally finite connected graphsX with infinitely many ends admitting a non-compact group of automorphisms which is transitive in its action on the space of ends, Ω X . For such a graphX, there is a uniquely determined biregular treeT (with both valencies finite), a continuous representationφ : Aut(X) → Aut(T) with compact kernel, an equivariant homeomorphism λ : Ω X → Ω T , and an equivariant map τ : Vert(X) → Vert(T) with finite fibers. Boundary-transitive trees are described, and some methods of constructing boundary-transitive graphs are discussed, as well as some examples.
KeywordsComplete Graph Maximal Subgroup Free Product Finite Graph Transitive Graph
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