Fornasiero, Federico; Naduvath, Sudev On \(J\)-colorability of certain derived graph classes. (English) Zbl 1439.05084 Acta Univ. Sapientiae, Inform. 11, No. 2, 159-173 (2019). Summary: A vertex \(v\) of a given graph \(G\) is said to be in a rainbow neighbourhood of \(G\), with respect to a proper coloring \(\mathcal{C}\) of \(G\), if the closed neighbourhood \(N[v]\) of the vertex \(v\) consists of at least one vertex from every color class of \(G\) with respect to \(\mathcal{C}\). A maximal proper coloring of a graph \(G\) is a \(J\)-coloring of \(G\) such that every vertex of \(G\) belongs to a rainbow neighbourhood of \(G\). In this paper, we study certain parameters related to \(J\)-coloring of certain Mycielski-type graphs. MSC: 05C15 Coloring of graphs and hypergraphs 05C38 Paths and cycles 05C75 Structural characterization of families of graphs Keywords:Mycielski graphs; graph coloring; rainbow neighbourhoods; \(J\)-coloring of graphs PDFBibTeX XMLCite \textit{F. Fornasiero} and \textit{S. Naduvath}, Acta Univ. Sapientiae, Inform. 11, No. 2, 159--173 (2019; Zbl 1439.05084) Full Text: DOI arXiv References: [1] J.A. Bondy, U.S.R. Murty, Graph theory, Springer, Berlin, 2008. ⇒159 · Zbl 1134.05001 [2] G. Chartrand, P. Zhang, Chromatic graph theory, CRC Press, Bocca Raton, 2009. ⇒159 · Zbl 1169.05001 [3] F. Harary, Graph theory, Narosa Publishing House, New Delhi, 2001. ⇒159 · Zbl 1020.05033 [4] T. R. Jensen, B. Toft, Graph coloring problems, John Wiley & Sons, 1995. ⇒159 · Zbl 0855.05054 [5] J. Kok, N. K. Sudev, U. Mary, On chromatic Zagreb indices of certain graphs, Discrete Math. Algorithm. Appl., 9, 1 (2017) 1750014:1-14, DOI: 10.1142/S1793830917500148. ⇒161 · Zbl 1358.05107 [6] J. Kok, N. K. Sudev, J-coloring of graph operations, Acta Univ. Sapientiae Inform., 11, 1 (2017) 95-108. ⇒161 · Zbl 1430.05042 [7] J. Kok, N. K. Sudev, M. K. Jamil, Rainbow neighbourhood number of graphs, Proyecciones J. Math., 39, 3 (2019) 469-485. ⇒161 · Zbl 1442.05060 [8] M. Kubale, Graph colorings, American Mathe. Soc., 2004. ⇒159 · Zbl 1064.05061 [9] W. Lin, J. Wu, P. C. B. Lam, G. Gu, Several parameters of generalized Mycielskians, Discrete Appl. Math., 154, 8 (2006) 1173-1182, DOI:10.1016/j.dam.2005.11.001. ⇒160 · Zbl 1093.05050 [10] N. K. Sudev, C. Susanth, S. J. Kalayathankal, J. Kok, A note on the rainbow neighbourhood number of graphs, Nat. Acd. Sci. Lett., 43, 2 (2019) 135-138. ⇒161 [11] N. K. Sudev, C. Susanth, S. J. Kalayathankal, J. Kok, Some new results on the rainbow neighbourhood number of graphs, Nat. Acd. Sci. Lett., 43, 2 (2019) 249-252. ⇒161 [12] N.K. Sudev, On certain J-coloring parameters of graphs, Nat. Acad. Sci. Lett., to appear. ⇒161, 162, 167 · Zbl 1400.05087 [13] C. Susanth, S.J. Kalayathankal, N.K. Sudev, Rainbow neighbourhood number of certain Mycielski type graphs, Int. J. Appl. Math., 31, 6 (2018) 797-803. ⇒161, 164 [14] A. Vince, Star chromatic number, J. Graph Theory12 (1988), 551-559. ⇒168 · Zbl 0658.05028 [15] D. B. West, Introduction to graph theory, Pearson Education Inc., 2001. ⇒159 [16] X. Zhu, The circular chromatic number: A survey, Disc. Math., 229, (2001) 371-410. ⇒168 · Zbl 0973.05030 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.