Brill-Noether locus of rank 1 and degree g-1 on a nodal curve

In this paper we consider the Brill-Noether locus $W_{\underset{‾}{d}}(C)$ of line bundles of multidegree $\underset{‾}{d}$ of total degree $g-1$ having a nonzero section on a nodal reducible curve $C$ of genus $g\ge 2$. We give an explicit description of the irreducible components of $W_{\underset{‾}{d}}(C)$ for a semistable multidegre $\underset{‾}{d}$. As a consequence we show that, if two semistable multidegrees of total degre $g-1$ on a curve with no rational components differ by a twister, then the respective Brill-Noether loci have isomorphic components.