RAINBOW CONNECTION NUMBER OF SOME WHEEL-RELATED GRAPHS

TitleRAINBOW CONNECTION NUMBER OF SOME WHEEL-RELATED GRAPHS
Publication TypeJournal Article
Year of Publication2019
AuthorsZAMORA, RINAB, BALDADO, JR., MICHAELP, PADUA, ROBERTON
Volume23
Issue1
Start Page31
Pagination20
Date Published11/2018
ISSN1083-2564
AMS05C15
Abstract

Let $f:E(G)\rightarrow\{1,2,...,k\}$ be an edge coloring of $G$, not necessarily proper. A path $P$ in $G$ is called a rainbow path if its edges have distinct colors. A graph $G$ is said to be rainbow-connected, if every two distinct vertices of $G$ is connected by a rainbow path. In this case, we say that $f$ is a rainbow $k$-coloring of $G$. The smallest $k$ such that $G$ has a rainbow $k$-coloring is called the rainbow connection number of $G$, denoted by $rc(G)$.

This study gave the rainbow connection number of lotus inside a circle, helms and sunflower graphs.
URLhttps://acadsol.eu/en/articles/23/1/3.pdf
DOI10.12732/caa.v23i1.3
Refereed DesignationRefereed
Full Text

[1] G. Chartrand, G. L. Johns, K. A. McKeon, P. Zhang, Rainbow connection in graphs, Math. Bohem. 133 (2008), 85-98.
[2] A. Kemnitz, I. Schiermeyer, Graphs with Rainbow Connection Number Equal to Two, Dicussiones Mathematicae Graph Theory 31 (2011) 313320.
[3] I. Schiermeyer, Bounds for Rainbow Connection Number of Graphs, Dicussiones Mathematicae Graph Theory 31 (2011) 387-395.
[4] M. Basavaraju, L.S. Chandran, D. Rjendraprasad, A. Ramaswamy, Rainbow Connection Number of Graph Power and Graph Product, arXiv:1104.4190v2[math.CO], 22 July 2011.
[5] A. Das, L.S. Chandran, D. Rjendraprasad, N.M. Varma, Rainbow Connection Number and Connected Dominating Sets, Journal of Graph Theory 71 (2012) 2, 206-218.
[6] X. Li, S. Liu, L.S. Chandran, D. Rjendraprasad, Rainbow Connection Number and Connectivity, The Electronic Journal of Combinatorics 19 (2012), 20.
[7] M. Basavaraju, L.S. Chandran, D. Rjendraprasad, A. Ramaswamy, Rainbow Connection Number and Radius. arXiv:1011.0620v2[math.CO], 11 Sept 2012.
[8] X. Li, Y. Sun, Rainbow Connection Number of Line Graphs, Ars Combin. 100 (2011), 449-463.
[9] M. Basavaraju, L.S. Chandran, D. Rajendraprasad, A. Ramaswamy, Rainbow connection number of graph power and graph products, Graphs Combin. (2013) http://dx.doi.org/10.1007/s00373-013-1355-3.
[10] T. Gologranc, G. Mekis, I. Peterin, Rainbow connection and graph products, Graphs Combin. (2013) http://dx.doi.org/10.1007/s00373-0131295-y.
[11] J. Ekstein, P. Holub, T. Kaiser, M. Koch, S.M. Camacho, Z. Rayj´a˘cek, I. Schiermeyer, The Rainbow Connection Number of 2-Connected Graphs, Discrete Math. 313 (2013) 19, 1884-1892.
[12] S. Sy, R. Wijaya, Surahmat, Applied Mathematical Sciences. Volume 94 (2014) 8, 4693-4696.
[13] M.A. Shulhany, A.N.M. Salman, The Strong Rainbow Connection Number of Stellar Graphs. AIP Conference Proceeding 1708, 050007(2015).
[14] D. Fitriani, A.N.M. Salman, Rainbow Connection Number of Amalgamation of Some Graphs. AKCE International Journal of Graphs and Combinatorics 13 (2016), 90-99.
[15] I.S. Kumala, A.N.M. Salman, The Rainbow Connection Number of a Flower (Cm,Kn) and a Flower (C3, Fn) Graph, Procedia Computer Science 74 (2015), 168-172.
[16] S. Sy, G.H. Medika, L. Yulianti, The Rainbow Connection Number of Fans and Suns, Applied Mathematical Sciences 7 (2013) 3155-3160.
[17] X. Li, Y. Shi, Y. Sun, Rainbow connection of graphs: a survey, Graphs Combin. 29 (1) (2013) 1-38.
[18] Y. Caro, A. Lev, Y. Roditty, Z. Tuza, R. Yuster, On rainbow connection, Electron. J. Combin. 15, 2008, R57.
[19] I. Schiermeyer, Rainbow connection in graphs with minimum degree three, In J. Fiala, J. Kratochvl, M. Miller, Ed., Combinatorial Algorithms, Lecture Notes in Computer Science Vol.5874 (2009), 432-437. Springer Berlin/Heidelberg.
[20] M. Krivelevich, R. Yuster, The rainbow connection of a graph is (at most) reciprocal to its minimum degree three, J. Graph Theory 63(3), 2009, pp. 185-191.
[21] M. Basavaraju, L.S. Chandran, D. Rajendraprasad, and A. Ramaswamy, Rainbow connection number and radius, Arxiv preprint arXiv:1011.0620v1
[math.CO], 2010.
[22] X. Li, Y. Shi, Rainbow connection in 3-connected graphs, arXiv:1010:6131v1
[math:CO] 2010.
[23] S. Nabila, A.N.M. Salman, The rainbow connection number of origami graphs and pizza graphs, Procedia Comput. Sci. 4 (2015) 162-167.
[24] D. Resty, A.N.M. Salman, The rainbow connection number of an ncrossed prism graph and its corona product with a trivial graph, Procedia Comput. Sci. 4 (2015) 143-150.
[25] D.N.S. Simamora, A.N.M. Salman, The rainbow (vertex) connection number of pencil graphs, Procedia Comput. Sci. 4 (2015) 138-142.
[26] M.A. Shulhany, A.N.M. Salman, The (strong) rainbow connection number of stellar graphs, in: Proceedings of International Seminar on Mathematics, Science, and Computer Science Education, MSCEIS 2015, AIP Conf. Proc. 1708, pp. 060007-1-060007.
[27] Susilawati, A.N.M Salman, Rainbow connection number of rocket graphs, in: The 5th International Conference on Mathematics and Natural Sciences, AIP Conf. Proc. 1677, 2015, pp. 030012-1-030012-3.
[28] A.B. Ericksen, A matter of security, Graduating Engineer & Computer Careers (2007) 24-28.
[29] J. Gross, J. Yellen, Handbook of Graph Theory, CRC Press LLC, N. W., Corporate Blvd, Boca Raton, Florida.
[30] R. Ponraj, S. Sathish Narayanan, R. Kala, Radio mean labeling of a graph, AKCE International Journal of Graphs and Combinatorics, 12 (2015) 224-228.