Two-ended regular median graphs |
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| Authors: | Wilfried Imrich Sandi Klav?ar |
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| Institution: | aMontanuniversität Leoben, A-8700 Leoben, Austria;bFaculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia;cFaculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, 2000 Maribor, Slovenia |
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| Abstract: | We show that regular median graphs of linear growth are the Cartesian product of finite hypercubes with the two-way infinite path. Such graphs are Cayley graphs and have only two ends.For cubic median graphs G the condition of linear growth can be weakened to the condition that G has two ends. For higher degree the relaxation to two-ended graphs is not possible, which we demonstrate by an example of a median graph of degree four that has two ends, but nonlinear growth. |
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| Keywords: | Median graphs Infinite graphs Cartesian product of graphs Ends of graphs Growth rate of graphs |
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