Abstract:
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.