  The motivation for this paper are computer calculations of complete lists of
weight systems of quasihomogeneous polynomials with isolated singularity at 0
up to rather large Milnor numbers. We review combinatorial characterizations of
such weight systems for any number of variables. This leads to certain types
and graphs of such weight systems. Using them, we prove an upper bound for the
common denominator (and the order of the monodromy) by the Milnor number, and
we show surprising consequences if the Milnor number is a prime number.
