On dynamic coloring of certain cycle-related graphs

Arabian Journal of Mathematics, Aug 2018

Coloring the vertices of a particular graph has often been motivated by its utility to various applied fields and its mathematical interest. A dynamic coloring of a graph G is a proper coloring of the vertex set V(G) such that for each vertex of degree at least 2, its neighbors receive at least two distinct colors. A dynamic k-coloring of a graph is a dynamic coloring with k colors. A dynamic k-coloring is also called a conditional (k, 2)-coloring. The smallest integer k such that G has a dynamic k-coloring is called the dynamic chromatic number \(\chi _d(G)\) of G. In this paper, we investigate the dynamic chromatic number for the line graph of sunlet graph and middle graph, total graph and central graph of sunlet graphs, paths and cycles. Also, we find the dynamic chromatic number for Mycielskian of paths and cycles and the join graph of paths and cycles. Open image in new window

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On dynamic coloring of certain cycle-related graphs

Arabian Journal of Mathematics pp 1–9 | Cite as On dynamic coloring of certain cycle-related graphs AuthorsAuthors and affiliations J. Vernold VivinN. MohanapriyaJohan KokM. Venkatachalam Open Access Article First Online: 23 August 2018 Received: 31 January 2018 Accepted: 07 August 2018 32 Downloads Abstract Coloring the vertices of a particular graph has often been motivated by its utility to various applied fields and its mathematical interest. A dynamic coloring of a graph G is a proper coloring of the vertex set V(G) such that for each vertex of degree at least 2, its neighbors receive at least two distinct colors. A dynamic k-coloring of a graph is a dynamic coloring with k colors. A dynamic k-coloring is also called a conditional (k, 2)-coloring. The smallest integer k such that G has a dynamic k-coloring is called the dynamic chromatic number \(\chi _d(G)\) of G. In this paper, we investigate the dynamic chromatic number for the line graph of sunlet graph and middle graph, total graph and central graph of sunlet graphs, paths and cycles. Also, we find the dynamic chromatic number for Mycielskian of paths and cycles and the join graph of paths and cycles. Open image in new window Mathematics Subject Classification05C15  Download to read the full article text Notes Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. References 1. Ahadi, A.; Akbari, S.; Dehghan, A.; Ghanbari, M.: On the difference between chromatic number and dynamic chromatic number of graphs. Discret. Math. 312, 2579–2583 (2012)MathSciNetCrossRefzbMATHGoogle Scholar 2. Akbari, S.; Ghanbari, M.; Jahanbakam, S.: On the dynamic chromatic number of graphs. Combinatorics and Graphs. In: Contemporary Mathematics-American Mathematical Society, vol. 531, pp. 11–18 (2010)Google Scholar 3. 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Vernold Vivin, J.: Harmonious coloring of total graphs, \(n\)-leaf, central graphs and circumdetic graphs, Bharathiar University, (2007), Ph.D Thesis, Coimbatore, IndiaGoogle Scholar Copyright information © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Authors and Affiliations J. Vernold Vivin1Email authorView author's OrcID profileN. Mohanapriya2Johan Kok3M. Venkatachalam21.Department of MathematicsUniversity College of Engineering Nagercoil, (Anna University Constituent College)NagercoilIndia2.Department of MathematicsKongunadu Arts and Science CollegeCoimbatoreIndia3.Licensing ServicesMetro Police Head OfficeTshwaneSouth Africa


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J. Vernold Vivin, N. Mohanapriya, Johan Kok, M. Venkatachalam. On dynamic coloring of certain cycle-related graphs, Arabian Journal of Mathematics, 2018, 1-9, DOI: 10.1007/s40065-018-0219-3