TL;DR
This paper introduces a specific vertex transitive, locally finite graph that is inaccessible and not quasi-isometric to any Cayley graph, challenging assumptions about the geometric properties of such graphs.
Contribution
The paper constructs an example of an inaccessible, vertex transitive, locally finite graph that defies quasi-isometric equivalence to Cayley graphs, highlighting new geometric phenomena.
Findings
The graph is vertex transitive and locally finite.
It is inaccessible, meaning it cannot be decomposed into simpler components.
It is not quasi-isometric to any Cayley graph.
Abstract
An inaccessible, vertex transitive, locally finite graph is described. This graph is not quasi-isometric to a Cayley graph.
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Taxonomy
TopicsAdvanced Graph Theory Research · Geometric and Algebraic Topology