RAINBOW VERTEX CONNECTION NUMBER OF BULL GRAPH, NET GRAPH, TRIANGULAR LADDER GRAPH, AND COMPOSITION GRAPH (P_n [P_1 ])

  • Muhammad Ilham Nurfaizi Annadhifi Departement of Mathematics Education - Universitas Jember, Indonesia
  • Robiatul Adawiyah Combinatorics, Graph Theory, and Network Topology – Universitas Jember, Indonesia https://orcid.org/0000-0002-8481-2932
  • Dafik Dafik Combinatorics, Graph Theory, and Network Topology – Universitas Jember, Indonesia
  • I Nengah Suparta Department of Mathematics Education, Universitas Pendidikan Ganesha, Indonesia
DOI: https://doi.org/10.30598/barekengvol18iss3pp1665-1672
Keywords: Rainbow Vertex Coloring, Rainbow Vertex Connection Number

Abstract

The rainbow connection was first introduced by Chartrand in 2006 and then in 2009 Krivelevich and Yuster first time introduced the rainbow vertex connection. Let graph  be a connected graph. The rainbow vertex-connection is the assignment of color to the vertices of a graph , if every vertex on the graph  is connected by a path graph that has interior vertices in different colors. The minimum number of colors from the rainbow vertex coloring in the graph  is called rainbow vertex connection number which is denoted . The results of the research are the rainbow vertex connection number of bull graph, net graph, triangular ladder graph, and graph composition (Pn[P1]).

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References

Dafik, Slamin, and A. Muharromah, “On the (Strong) Rainbow Vertex Connection of Graphs Resulting from Edge Comb Product,” J. Phys. Conf. Ser., vol. 1008, no. 1, 2018, doi: 10.1088/1742-6596/1008/1/012055.

Y. Hou and W. C. Shiu, “The spectrum of the edge corona of two graphs,” Electron. J. Linear Algebr., vol. 20, no. September, pp. 586–594, 2010, doi: 10.13001/1081-3810.1395.

D. B. Nugroho, “Catatan Kuliah (2 sks) MX 324 Pengantar Teori Graf (,” 2008.

G. Chartrand, D. Erwin, P. Zhang, and M. Bohemica, “Mathematica Bohemica Terms of use :,” vol. 127, no. 1, pp. 85–98, 2002.

D. Estetikasari and S. Sy, “On the rainbow connection for some corona graphs,” Appl. Math. Sci., vol. 7, no. 97–100, pp. 4975–4980, 2013, doi: 10.12988/ams.2013.37410.

Y. Caro, A. Lev, Y. Roditty, Z. Tuza, and R. Yuster, “On rainbow connection,” Electron. J. Comb., vol. 15, no. 1 R, pp. 1–13, 2008, doi: 10.37236/781.

M. Krivelevich and R. Yuster, “The rainbow connection of a graph is (at most) reciprocal to its minimum degree,” J. Graph Theory, vol. 63, no. 3, pp. 185–191, 2010, doi: 10.1002/jgt.20418.

P. Heggernes, D. Issac, J. Lauri, P. T. Lima, and E. J. Van Leeuwen, “Rainbow vertex coloring bipartite graphs and chordal graphs,” Leibniz Int. Proc. Informatics, LIPIcs, vol. 117, no. 83, pp. 1–13, 2018, doi: 10.4230/LIPIcs.MFCS.2018.83.

X. Li and Y. Shi, “On the rainbow vertex-connection 1,” vol. 33, pp. 307–313, 2013, doi: 10.7151/dmgt.1664.

X. Li and S. Liu, “Rainbow vertex-connection number of 2-connected graphs ∗,” no. 11071130, pp. 1–10.

H. Lei, S. Li, H. Liu, and Y. Shi, “Rainbow vertex connection of digraphs,” J. Comb. Optim., vol. 35, no. 1, pp. 86–107, 2018, doi: 10.1007/s10878-017-0156-7.

J. Ekstein et al., “The rainbow connection number of 2-connected graphs,” Discrete Math., vol. 313, no. 19, pp. 1884–1892, 2013, doi: 10.1016/j.disc.2012.04.022.

K. Munawaroh, A. I. Kristiana, E. R. Albirri, D. Dafik, and R. Adawiyah, “Pewarnaan Titik Ketakteraturan Lokal pada Keluarga Graf Unicyclic,” Cgant J. Math. Appl., vol. 2, no. 2, pp. 6–21, 2022, doi: 10.25037/cgantjma.v2i2.59.

N. Azahra, “Pewarnaan Titik Ketakteraturan Lokal pada Keluarga Graf Grid dan Keterkaitannya dengan Keterampilan Berpikir Tingkat Tinggi,” 2020.

A. Muharromah, “On the ( Strong ) Rainbow Vertex Connection of Graphs Resulting from Edge Comb Product” 2018.

Published
2024-07-31
How to Cite
[1]
M. Annadhifi, R. Adawiyah, D. Dafik, and I. Suparta, “RAINBOW VERTEX CONNECTION NUMBER OF BULL GRAPH, NET GRAPH, TRIANGULAR LADDER GRAPH, AND COMPOSITION GRAPH (P_n [P_1 ])”, BAREKENG: J. Math. & App., vol. 18, no. 3, pp. 1665-1672, Jul. 2024.
Issue
Vol 18 No 3 (2024): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2024 Muhammad Ilham Nurfaizi Annadhifi, Robiatul Adawiyah, Dafik Dafik, I Nengah Suparta

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