|
In this talk it is shown that regular median graphs of linear growth are the
Cartesian product of finite hypercubes with the two-way infinite
path. Such graphs are vertex transitive, in fact, they even 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.
However, for higher degree the relaxation to two-ended graphs not possible
any more, which is shown by an example of a median graph
of degree four that has two ends, but nonlinear growth.
|