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.
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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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Imrich, W., Klavžar, S. Transitive, Locally Finite Median Graphs with Finite Blocks. Graphs and Combinatorics 25, 81–90 (2009). https://doi.org/10.1007/s00373-008-0828-2
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DOI: https://doi.org/10.1007/s00373-008-0828-2