Locally finite homogeneous graphs

Abstract

A connected graph G is said to be z-homogeneous if any isomorphism between finite connected induced subgraphs of G extends to an automorphism of G. Finite z-homogeneous graphs were classified in [17]. We show that z-homogeneity is equivalent to finite-transitivity on the class of infinite locally finite graphs. Moreover, we classify the graphs satisfying these properties. Our study of bipartite z-homogeneous graphs leads to a new characterization for hypercubes.

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Correspondence to Shawn Hedman.

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Hedman, S., Pong, W.Y. Locally finite homogeneous graphs. Combinatorica 30, 419–434 (2010). https://doi.org/10.1007/s00493-010-2472-8

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Mathematics Subject Classification (2000)

  • 05C75