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\iteman{io-port 05925111}
\itemau{Reddy, P.Siva Kota; Shivashankara, K.; Madhusudhan, K.V.}
\itemti{Negation switching equivalence in signed graphs.}
\itemso{Int. J. Math. Comb. 3, 85-90 (2010).}
\itemab
Summary: A Smarandachely $k$-signed graph (Smarandachely $k$-marked graph) is an ordered pair $S= (G,\sigma)$ ($S= (G,\mu)$), where $G= (V,E)$ is a graph called underlying graph of $S$ and $\sigma: E\to(\overline e_1,\overline e_2,\dots,\overline e_k)$ ($\mu: V\to(\overline e_1,\overline e_2,\dots,\overline e_k)$) is a function, where each $\overline e_i\in\{+,-\}$. Particularly, a Smarandachely 2-signed graph or Smarandachely 2-marked graph is called abbreviated a signed graph or a marked graph. In this paper, we establish a new graph equation $L^2(G)\cong L^k(G)$, where $L^2(G)\,\&\,L^k(G)$ are second iterated line graph and $k$th iterated line graph respectively. Further, we characterize signed graphs $S$ for which $L^2(S)\sim L^k(S)$ and $\eta(S)\sim L^k(S)$, where $\sim$ denotes switching equivalence and $L^2(S)$, $L^k(S)$ and $\eta(S)$ are denotes the second iterated line signed graph, $k$th iterated line signed graph and negation of $S$, respectively.
\itemrv{~}
\itemcc{}
\itemut{Smarandachely $k$-signed graphs; Smarandachely $k$-marked graphs; signed graphs; marked graphs; balance; switching; line signed graphs; negation}
\itemli{}
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