# Imprimitivity of locally finite, 1-ended, planar graphs

@article{Sirn2012ImprimitivityOL, title={Imprimitivity of locally finite, 1-ended, planar graphs}, author={Jozef Sir{\'a}n and Mark E. Watkins}, journal={Ars Math. Contemp.}, year={2012}, volume={5}, pages={217-221} }

Using results from group theory, we offer a concise proof of the imprimitivity of locally finite, vertex-transitive, 1-ended planar graphs, a result previously established by J. E. Graver and M. E. Watkins (2004) using graph-theoretical methods.

## One Citation

Lobe, edge, and arc transitivity of graphs of connectivity 1

- MathematicsArs Math. Contemp.
- 2019

It is shown that, given any biconnected graph $\Lambda$ and a "code" assigned to each orbit of Aut, there exists a unique lobe-transitive graph $\Gamma$ of connectivity 1 whose lobes are copies of $\Lamba$ and is consistent with the given code at every vertex of $\gamma$.

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