# Negation Switching Invariant Signed Graphs

Sinha, Deepa • Dhama, Ayushi

## Abstract

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.

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