05953188

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05953188 Reddy, P.Siva Kota Rangarajan, R. Subramanya, M.S. Switching invariant neighborhood signed graphs. Proc. Jangjeon Math. Soc. 14, No. 2, 249-258 (2011). 2011 Jangjeon Research Institute for Mathematical Sciences \& Physics, Daegu; Jangjeon Mathematical Society, Kyungshang Nam-Do EN marked graph Summary: A signed graph (marked graph is an ordered pair $S= (G,\sigma)$ ($S= (G,\mu)$), where $G= (V,E)$ is a graph called the underlying graph of $S$ and $\sigma: E\to\{+,-\}$ ($\mu: V\to \{+,-\}$) is a function. The neighborhood graph of a graph $G= (V,E)$, denoted by $N(G)$, is a graph on the same vertex set $V$, where two vertices in $N(G)$ are adjacent if, and only if, they have a common neighbor. Analogously, one can define the neighborhood signed graph $N(S)$ of a signed graph $S= (G,\sigma)$ as a signed graph, $N(S)= (N(G),\sigma')$, where $N(G)$ is the underlying graph of $N(S)$, and for any edge $e= uv$ in $N(S)$, $\sigma'(e)= \mu(u)\mu(v)$, where for any $v\in V$, $\mu(v)= \prod_{u\in N(v)}\sigma(uv)$. In this paper, we characterize signed graphs $S$ for which $S\sim N(S)$, $S^c\sim N(S)$ and $N(S)\sim J(S)$, where $J(S)$ and $S^c$ denotes jump signed graph and complement of signed graph of $S$, respectively.