Title: Possible heights of graph transformation groups,
Abstract: In the following text we prove that for all finite $p\geq0$ there exists a
topological graph $X$ such that $\{p,p+1,p+2,\ldots\}\cup\{+\infty\}$ is the
collection of all possible heights for transformation groups with phase space
$X$. Moreover for all topological graph $X$ with $p$ as height of
transformation group $(Homeo(X),X)$, $\{p,p+1,p+2,\ldots\}\cup\{+\infty\}$
again is the collection of all possible heights for transformation groups with
phase space $X$.