Signed Graphs and Hushimi Trees

The operation of local switching is introduced by Cameron，Seidel
and Tsaranov. It acts on the set of all signed graphs on n vertices.
In this paper，mainly，we study how local switching acts on
trees. We show that two trees on the same vertices are isomorphic
if and only if one is transformed to the other by a sequence of local
switchings. There is a correspondence between signed graphs and
a root lattice. Any signed graph corresponding to the lattice An is
transformed by a sequence of local switchings to the tree which is
regarded as the Dynkin diagram of An.