An Alexander polynomial for MOY graphs

We introduce an Alexander polynomial for MOY graphs. For a framed trivalent MOY graph G, we refine the construction and obtain a framed ambient isotopy invariant Delta((G,c))(t). The invariant Delta((G,c))(t) satisfies a series of relations, which we call MOY-type relations, and conversely these relations determine Delta((G,c))(t). Using them we provide a graphical definition of the Alexander polynomial of a link. Finally, we discuss some properties and applications of our invariants.