Matsumoto theorem for skeleta

We present a proof of a generalization of the theorem of H. Matsumoto on Coxeter groups. Our generalized version is applicable to “graphs admitting geometric realization”. The original version of the theorem for Coxeter groups is a special case when applied to the Cayley graph and the geometric representation of a Coxeter group. Our version of Matsumoto theorem is also applicable to skeleta , graphs that were defined in the recent paper [GHS24] on root Lie superalgebras.