We give a combinatorial representation of compact
connected orientable 3-dimensional manifolds with boundary and
their special spines by a class of graphs with extrastructure which
are strictly related to o-graphs defined and studied in [3] and [4].
Then we describe a simple algorithm for constructing the boundary of these manifolds by using a list of 6-tuples of non-negative
integers. Finally we discuss some combinatorial methods for determining the hyperbolicity equations. Examples of hyperbolic 3-
manifolds of low complexity illustrate in particular cases the constructions and algorithms presented in the paper.
