Negation switching invariant signed graphs

Deepa Sinha (Associate Professor, Department of Mathematics South Asian University Akbar Bhawan Chanakyapuri, New Delhi 110021 (India) Cell No: [phone] E-Mail: [e-mail] [e-mail])
Ayushi Dhama (Centre for Mathematical Sciences, Banasthali University, Banasthali-304 022 Rajasthan)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 2, No 1 (2014): Electronic Journal of Graph Theory and Applications

A signed graph (or, $sigraph$ in short) is a graph G in which each edge x carries a value $\sigma(x) \in \{-, +\}$ called its sign. Given a sigraph S, the negation $\eta(S)$ 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 $\eta (S)$ are signed isomorphic.