  The Reeb space of a smooth function is a topological and combinatoric object
and fundamental and important in understanding topological and geometric
properties of the manifold of the domain. It is the graph and a topological
space endowed with a natural topology. This is defined as the quotient space of
the manifold of the domain where the equivalence relation is as follows: two
points in the manifold are equivalent if and only if they are in a same
connected component of a level set or a preimage. In considerable cases they
are graphs (Reeb graphs): if the function is a so-called Morse(-Bott) functions
for example, then this is the graph such that a point is a vertex if and only
if the corresponding connected component of the level set contains some
singular points.
  The author previously constructed explicit smooth functions on suitable
3-dimensional connected, closed and orientable manifolds whose Reeb graphs are
isomorphic to prescribed graphs and whose preimages are as prescribed types.
This gives a new answer to so-called realization problems of graphs as Reeb
graphs of smooth functions of suitable classes. The present paper concerns a
variant in the case where the 3-dimensional manifolds may not be non-orientable
extending the result before. \end{abstract}
