Negation switching invariant signed graphs - Deepa Sinha; Ayushi Dhama (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2014)
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 S_1 and S_2 on the same underlying graph are switching equivalent if it is possible to assign signs `+' (`plus') or `-' (`minus') to vertices of S_1 such that by reversing the sign of each of its edges that has received opposite signs at its ends, one obtains S_2. In this paper, we characterize sigraphs which are negation switching invariant and also see for what sigraphs, S and η (S) are signed isomorphic.