  For any given graph G = (V,E) we define in a certain way a new graph G(x,y,z)
with the vertex set V\cup E depending on parameters x,y,z from {0,1, +, -} and
call graph G(x,y,z) the (x,y,z)-transformation of G. It turns out that if G is
an r-regular graph, then the Laplacian polynomial of G(x,y,z) is a function of
|V|, r, and the Laplacian spectrum of G. We give a complete description of this
function.
