Characterizations of line graphs in signed and gain graphs

We generalize three classical characterizations of line graphs to signed and gain graphs: the Krausz's characterization, van Rooij Wilf's characterization Beineke's characterization. In particular, we present a list forbidden subgraphs characterizing class gain-line graphs. case graph whose underlying is graph, this consists exactly four Under same hypothesis, prove that if only its eigenvalues are either greater than $-2$, or less $2$, depending on which particular definition adopted.