Combinatorica

, Volume 30, Issue 4, pp 419–434

Locally finite homogeneous graphs

Article

DOI: 10.1007/s00493-010-2472-8

Cite this article as:
Hedman, S. & Pong, W.Y. Combinatorica (2010) 30: 419. doi:10.1007/s00493-010-2472-8

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

Copyright information

© János Bolyai Mathematical Society and Springer Verlag 2010

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceFlorida Southern CollegeLakelandUSA
  2. 2.Department of MathematicsCalifornia State University Dominguez HillsCarsonUSA