Signed Graphs and Hushimi Trees

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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.

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