Two-ended regular median graphs

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 twoended graphs is not possible, which we demonstrate by an example of a median graph of degree four that has two ends, but nonlinear growth. Key words: Median graphs; infinite graphs; Cartesian product of graphs; ends of graphs; growth rate of graphs AMS subject classification (2010): 05C63, 05C75

• Type: Journal
• Year: 2011
• Where: DM
• Authors: Wilfried Imrich, Sandi Klavzar
• Keywords: Automated Reasoning, Cartesian Product, Cayley Graphs, DM 2011, Median Graphs