Shao, Yehong Connectivity of iterated line graphs. (English) Zbl 1215.05097 Discrete Appl. Math. 158, No. 18, 2081-2087 (2010). Summary: Let \(k\geq 0\) be an integer and \(L^k(G)\) be the \(k\)th iterated line graph of a graph \(G\). Niepel and Knor proved that if \(G\) is a 4-connected graph, then \(\kappa (L^{2}(G))\geq 4\delta (G) - 6\). We show that the connectivity of \(G\) can be relaxed. In fact, we prove in this note that if \(G\) is an essentially 4-edge-connected and 3-connected graph, then \(\kappa (L^{2}(G))\geq 4\delta (G) - 6\). Similar bounds are obtained for essentially 4-edge-connected and 2-connected (1-connected) graphs. Cited in 5 Documents MSC: 05C40 Connectivity 05C76 Graph operations (line graphs, products, etc.) Keywords:connectivity; essential edge connectivity; iterated line graph PDF BibTeX XML Cite \textit{Y. Shao}, Discrete Appl. Math. 158, No. 18, 2081--2087 (2010; Zbl 1215.05097) Full Text: DOI References: [1] Bondy, J.A.; Murty, U.S.R., Graph theory with applications, (1976), Macmillan London, Elsevier, New York · Zbl 1134.05001 [2] Chartrand, G.; Stewart, M.J., The connectivity of line graphs, Math. ann., 182, 170-174, (1969) · Zbl 0167.52203 [3] Knor, M.; Niepel, L’., Connectivity of iterated line graphs, Discrete appl. math., 125, 255-266, (2003) · Zbl 1009.05086 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.