On dynamic colouring of cartesian product of complete graph with some graphs
A proper vertex colouring is called a 2-dynamic colouring, if for every vertex v with degree at least 2, the neighbours of v receive at least two colours. The smallest integer k such that G has a dynamic colouring with k colours denoted by $\chi _2(G) $. We denote the cartesian product of G and H by...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2020-01-01
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| Series: | Journal of Taibah University for Science |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/16583655.2020.1713586 |
| _version_ | 1818953482111025152 |
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| author | K. Kaliraj H. Naresh Kumar J. Vernold Vivin |
| author_facet | K. Kaliraj H. Naresh Kumar J. Vernold Vivin |
| author_sort | K. Kaliraj |
| collection | DOAJ |
| description | A proper vertex colouring is called a 2-dynamic colouring, if for every vertex v with degree at least 2, the neighbours of v receive at least two colours. The smallest integer k such that G has a dynamic colouring with k colours denoted by $\chi _2(G) $. We denote the cartesian product of G and H by $G\Box H $. In this paper, we find the 2-dynamic chromatic number of cartesian product of complete graph with complete graph $K_{r} \Box K_{s} $, complete graph with complete bipartite graph $K_n \Box K_{1,s} $ and wheel graph with complete graph $W_l \Box K_n $. |
| first_indexed | 2024-12-20T10:06:58Z |
| format | Article |
| id | doaj.art-a9660afe5c0b4ba2a79a8b55d91f5b63 |
| institution | Directory Open Access Journal |
| issn | 1658-3655 |
| language | English |
| last_indexed | 2024-12-20T10:06:58Z |
| publishDate | 2020-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Taibah University for Science |
| spelling | doaj.art-a9660afe5c0b4ba2a79a8b55d91f5b632022-12-21T19:44:13ZengTaylor & Francis GroupJournal of Taibah University for Science1658-36552020-01-0114116817110.1080/16583655.2020.17135861713586On dynamic colouring of cartesian product of complete graph with some graphsK. Kaliraj0H. Naresh Kumar1J. Vernold Vivin2Ramanujan Institute for Advanced Study in Mathematics, University of MadrasRamanujan Institute for Advanced Study in Mathematics, University of MadrasDepartment of Mathematics, University College of Engineering Nagercoil (Anna University Constituent College)A proper vertex colouring is called a 2-dynamic colouring, if for every vertex v with degree at least 2, the neighbours of v receive at least two colours. The smallest integer k such that G has a dynamic colouring with k colours denoted by $\chi _2(G) $. We denote the cartesian product of G and H by $G\Box H $. In this paper, we find the 2-dynamic chromatic number of cartesian product of complete graph with complete graph $K_{r} \Box K_{s} $, complete graph with complete bipartite graph $K_n \Box K_{1,s} $ and wheel graph with complete graph $W_l \Box K_n $.http://dx.doi.org/10.1080/16583655.2020.1713586dynamic colouringcartesian productjoin and wheel |
| spellingShingle | K. Kaliraj H. Naresh Kumar J. Vernold Vivin On dynamic colouring of cartesian product of complete graph with some graphs Journal of Taibah University for Science dynamic colouring cartesian product join and wheel |
| title | On dynamic colouring of cartesian product of complete graph with some graphs |
| title_full | On dynamic colouring of cartesian product of complete graph with some graphs |
| title_fullStr | On dynamic colouring of cartesian product of complete graph with some graphs |
| title_full_unstemmed | On dynamic colouring of cartesian product of complete graph with some graphs |
| title_short | On dynamic colouring of cartesian product of complete graph with some graphs |
| title_sort | on dynamic colouring of cartesian product of complete graph with some graphs |
| topic | dynamic colouring cartesian product join and wheel |
| url | http://dx.doi.org/10.1080/16583655.2020.1713586 |
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