Transitive,Locally Finite Median Graphs with Finite Blocks |
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Authors: | Wilfried Imrich Sandi Klavžar |
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Institution: | 1.Montanuniversit?t Leoben,Leoben,Austria;2.Faculty of Mathematics and Physics,University of Ljubljana,Ljubljana,Slovenia |
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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.
Sandi Klavžar: Supported by the Ministry of Science of Slovenia under the grant P1-0297. The author is also with the Faculty
of Mathematics and Natural Sciences, University of Maribor, Slovenia and the Institute of Mathematics, Physics and Mechanics,
Ljubljana. |
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Keywords: | Median graphs Infinite graphs Vertex-transitive graphs |
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