Signed Graphs Associated with the Lattice A_n

For any base of the root lattice A_n, we can construct a signed graph naturally. A connected graph is called a Fushimi tree if its all blocks are complete subgraphs. In the present note, a Fushimi tree is said to be simple when by deleting any cut vertex, we have always two its connected components. We prove that a signed graph corresponding to a base of A_n is a simple Fushimi tree. Cameron, Seidel and Cameron [3] defined local switchings of singned graphs. We also show that a simple Fushimi tree is transformed to a line by a sequence of local switchngs.

公開日:2010年1月24日で登録したコンテンツは、国立情報学研究所において電子化したものです。