Note on neighborhood signed graphs and jump signed graphs
type: Item
instance of: scholarly article
zbMATH Open document ID: 1305.05096
author: P. Siva Kota Reddy
author: U. K. Misra
author: P. S. Hemavathi
publication date: 2014-11-10T00:00:00Z
Mathematics Subject Classification ID: 05C22
Mathematics Subject Classification ID: 05C76
zbMATH DE Number: 6367646
zbMATH Keywords: neighborhood graphs
zbMATH Keywords: iterated line graphs
zbMATH Keywords: jump graphs
zbMATH Keywords: signed graphs
zbMATH Keywords: balance
zbMATH Keywords: switching
zbMATH Keywords: neighborhood signed graphs
zbMATH Keywords: jump signed graph
MaRDI profile type: Publication
title: Note on neighborhood signed graphs and jump signed graphs
published in: Advanced Studies in Contemporary Mathematics (Kyungshang)
review text: 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.
reviewed by: V. Lokesha
description: scientific article; zbMATH DE number 6367646