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Locally finite homogeneous graphs

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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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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Florida Southern College, 111 Lake Hollingsworth Drive, Lakeland, FL, 33801, USA

    Shawn Hedman

  2. Department of Mathematics, California State University Dominguez Hills, 1000 E Victoria Street, Carson, California, 90747, USA

    Wai Yan Pong

Authors
  1. Shawn Hedman
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  2. Wai Yan Pong
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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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  • DOI: https://doi.org/10.1007/s00493-010-2472-8

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