Graphs and Combinatorics

, Volume 25, Issue 1, pp 81–90 | Cite as

Transitive, Locally Finite Median Graphs with Finite Blocks

Article

Abstract

The subject of this paper are infinite, locally finite, vertex-transitive median graphs. It is shown that the finiteness of the Θ-classes of such graphs does not guarantee finite blocks. Blocks become finite if, in addition, no finite sequence of Θ-contractions produces new cut-vertices. It is proved that there are only finitely many vertex-transitive median graphs of given finite degree with finite blocks. An infinite family of vertex-transitive median graphs with finite intransitive blocks is also constructed and the list of vertex-transitive median graphs of degree four is presented.

Keywords

Median graphs Infinite graphs Vertex-transitive graphs 

AMS Subject Classification (2000)

05C75 05C12 

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Copyright information

© Springer Japan 2009

Authors and Affiliations

  1. 1.Montanuniversität LeobenLeobenAustria
  2. 2.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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