  We study an inverse spectral problem for arbitrary order ordinary
differential equations on compact star-type graphs when differential equations
have regular singularities at boundary vertices. As the main spectral
characteristics we introduce and study the so-called Weyl-type matrices which
are generalizations of the Weyl function (m-function) for the classical
Sturm-Liouville operator. We provide a procedure for constructing the solution
of the inverse problem and prove its uniqueness.
