Eigenspaces for \(-2\) in signed line graphs

Abstract

It is known that \(-2\) appears in the spectrum of a connected signed line graph if and only if its root is either (a) a balanced signed graph, not a tree, that spans a switching of the complete signed graph or (b) an unbalanced simply signed graph, not a unicyclic simply signed graph, that spans a switching of the signed doubled complete graph. In this paper, we compute the eigenspaces for $-2$ of these signed line graphs. The contribution can be seen as an alternative to [Discrete Appl. Math. 207 (2016) 29--38].