Tilings and patterns
A note on the growth of transitive graphs
Discrete Mathematics - Proceedings of the Oberwolfach Meeting "Kombinatorik," January 19-25, 1986
Separating double rays in locally finite planar graphs
Discrete Mathematics
Geodetic rays and fibers in one-ended planar graphs
Journal of Combinatorial Theory Series B
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It is shown that the automorphism group of an infinite, locally finite, planar graph acts primitively on its vertex set if and only if the graph has connectivity 1 and, for some integer m ≥ 2, every vertex is incident with exactly m lobes, all of which are finite. Specifically, either all of the lobes are isomorphic to K4 or all are circuits of length p for some odd prime p.