Negation switching invariant signed graphs

A signed graph (or, sigraph in short) is a graph G in which each edge x carries a value σ(x) ∈ {−, +} called its sign. Given a sigraph S, the negation η(S) of the sigraph S is a sigraph obtained from S by reversing the sign of every edge of S. Two sigraphs S1 and S2 on the same underlying graph are switching equivalent if it is possible to assign signs ‘+’ (‘plus’) or ‘−’ (‘minus’) to vertices of S1 such that by reversing the sign of each of its edges that has received opposite signs at its ends, one obtains S2. In this paper, we characterize sigraphs which are negation switching invariant and also see for what sigraphs, S and η(S) are signed isomorphic.