  A signed graph is a graph whose edges are signed. In a vertex-signed graph
the vertices are signed. The latter is called consistent if the product of
signs in every circle is positive. The line graph of a signed graph is
naturally vertex-signed. Based on a characterization by Acharya, Acharya, and
Sinha in 2009, we give constructions for the signed simple graphs whose
naturally vertex-signed line graph is consistent.
