An irregular assignement of G is labelling f: E \ra \{1,2,...,m\} of the
edge-set of G such that all of the induced vertex labels computed as
\sigma_{v\in e}f(e) are distinct. The minimal number m for which this
is possible is called the minimal irregularity strength s_{m}(G) of G.
The case where all paths are of length 2 is conidered by Aigner and
Triesch by using decomposition of additive group Z_m. In this paper we
have invesitgated irregular assignments of the forest of paths of regular
and irregular lengths.