Article

Combinatorica

, Volume 30, Issue 4, pp 419-434

First online:

Locally finite homogeneous graphs

  • Shawn HedmanAffiliated withDepartment of Mathematics and Computer Science, Florida Southern College Email author 
  • , Wai Yan PongAffiliated withDepartment of Mathematics, California State University Dominguez Hills

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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.

Mathematics Subject Classification (2000)

05C75