  We investigate a graph parameter called the total vertex irregularity
strength ($tvs(G)$), i.e. the minimal $s$ such that there is a labeling $w:
E(G)\cup V(G)\rightarrow \{1,2,..,s\}$ of the edges and vertices of $G$ giving
distinct weighted degrees $wt_G(v):=w(v)+\sum_{v\in e \in E(G)}w(e)$ for every
pair of vertices of $G$. We prove that $tvs(F)=\lceil (n_1+1)/2 \rceil$ for
every forest $F$ with no vertices of degree 2 and no isolated vertices, where
$n_1$ is the number of pendant vertices in $F$. Stronger results for trees were
recently proved by Nurdin et al.
