Note on neighborhood signed graphs and jump signed graphs (Q2928726)

For any graph \(\Gamma\), the neighborhood graph \(N(\Gamma)\) of \((\Gamma)\) is a graph on the same vertex set \(V(\Gamma)\), for which two vertices are adjacent if, and only if, they have a common neighbor. Neighborhood graphs are also known as 2-path graphs.NEWLINENEWLINENEWLINE The authors characterize the graphs for which \(N(\Gamma)\cong L^2(\Gamma)\) and \(N(\Gamma)\cong J(\Gamma)\) where \(N(\Gamma)\) is a neighbourhood graph, \(L^2(\Gamma)\) is a 2nd iterated line graph, and \(J(\Gamma)\) is a jump graph of a graph \(\Gamma\). Using these concepts, the authors establish analogously the corresponding switching equivalence characterizations. Also, they remark the possible solutions for \(N(\Sigma)\cong J(\Sigma)\) where \(N(\Sigma)\) is a neighborhood signed graph and \(J(\Sigma)\) is a jump signed graph of a signed graph \(\Sigma\).NEWLINENEWLINENEWLINE This work is useful to researchers working in the area of signed graphs.