TL;DR
This paper explores the structure of infinite, connected graphs with multiple ends, revealing that end-transitive graphs and those with certain stabilizer properties exhibit a tree-like structure.
Contribution
It characterizes the structure of infinite, connected graphs with multiple ends, focusing on end-transitivity and stabilizer actions, showing they are tree-like.
Findings
End-transitive graphs with infinitely many ends are tree-like.
Graphs with stabilizer of an end acting transitively are also tree-like.
The study extends understanding of infinite graph symmetries and their structural implications.
Abstract
We investigate the structure of connected graphs, not necessarily locally finite, with infinitely many ends. On the one hand we study end-transitive such graphs and on the other hand we study such graphs with the property that the stabilizer of some end acts transitively on the vertices of the graph. In both cases we show that the graphs have a tree-like structure.
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Taxonomy
TopicsAdvanced Graph Theory Research · Rings, Modules, and Algebras · semigroups and automata theory