RAINBOW VERTEX-CONNECTION NUMBER ON COMB PRODUCT OPERATION OF CYCLE GRAPH (C_4) AND COMPLETE BIPARTITE GRAPH (K_(3,N))

  • Nisky Imansyah Yahya Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Negeri Gorontalo, Indonesia
  • Ainun Fatmawati Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Negeri Gorontalo, Indonesia
  • Nurwan Nurwan Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Negeri Gorontalo, Indonesia
  • Salmun K Nasib Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Negeri Gorontalo, Indonesia
DOI: https://doi.org/10.30598/barekengvol17iss2pp0673-0684
Keywords: Rainbow Vertex-Connection Number, Comb Product Operation, Cycle Graph, Complete Bipartite Graph

Abstract

Rainbow vertex-connection number is the minimum colors assignment to the vertices of the graph, such that each vertex is connected by a path whose edges have distinct colors and is denoted by . The rainbow vertex connection number can be applied to graphs resulting from operations. One of the methods to create a new graph is to perform operations between two graphs. Thus, this research uses comb product operation to determine rainbow-vertex connection number resulting from comb product operation of cycle graph and complete bipartite graph  & . The research finding obtains the theorem of rainbow vertex-connection number at the graph of  for  while the theorem of rainbow vertex-connection number at the graph of  for  for .

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References

D. S. Zaenab, D. A. Adyanti, A. Fanani, and N. Ulinnuha, “Aplikasi Graph Coloring Pada Penjadwalan Perkuliahan Di Fakultas Sains Dan Teknologi Uin Sunan Ampel Surabaya,” Jurnal Matematika “MANTIK,” vol. 2, no. 1, p. 30, 2016, doi: 10.15642/mantik.2016.2.1.30-39.

A. Verma, A. Asthana, and S. Gupta, “Using Graph Theory for Automated Electric Network Solving and Analysis”, doi: 10.13140/RG.2.2.16919.50087.

J. Vrbik, “Solving Electrical Circuits via Graph Theory,” Appl Math (Irvine), vol. 13, no. 01, pp. 77–86, 2022, doi: 10.4236/am.2022.131007.

N. Irawati and R. Heri, “Pelabelan Total Titik Ajaib Pada Complete Graph,” Matematika, vol. 13, no. 3, 2010.

Y. Joko and F. Fran, “Bilangan Terhubung Pelangi pada Graf,” Bimaster, vol. 08, no. 1, pp. 29–34, 2019.

D. Rahmawati, F. Fran, and Helmi, “Bilangan Terhubung Total Pelangi pada Graf Garis dan Double Graf Garis dari Graf Sikat,” Bimaster, vol. 09, no. 2, pp. 319–328, 2020.

G. Chartrand, Kalamazoo, G. L. Johns, and S. Valley, “Rainbow Connection In Graphs,” Mathematica Bohemica, vol. 133, no. 1, pp. 85–98, 2008.

G. Chartrand, G. L. Johns, K. A. Mckeon, and P. Zhang, “Rainbow Connection in Graphs,” vol. 133, no. 1, pp. 85–98, 2008.

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.

F. A. Saputra, “Bilangan Rainbow Connection dari Hasil Operasi Penjumlahan dan Perkalian Kartesius Dua Graf,” Cauchy, vol. 2, no. 3, pp. 125–138, 2012.

H. Li, Y. Ma, and Y. Zhao, “Total Rainbow Connection Number of Some Graph Operations,” Axioms, vol. 11, no. 6, Jun. 2022, doi: 10.3390/axioms11060254.

Y. Yuri, “Penentuan Rainbow Connection Number pada Hasil Operasi Cartesian Product,” Matematika Unad, vol. VI, no. 1, pp. 148–152.

Y. Hastuti, Dafik, I. H. Agustin, R. M. Prihandini, and R. Alfarisi, “The total rainbow connection on comb product of cycle and path graphs,” IOP Conf Ser Earth Environ Sci, vol. 243, no. 1, 2019.

D. Fitriani, A. Salman, and Z. Y. Awanis, “Rainbow connection number of comb product of graphs,” Electronic Journal of Graph Theory and Applications, vol. 10, no. 2, p. 461, Sep. 2022, doi: 10.5614/ejgta.2022.10.2.9.

D. Dafik, S. Slamin, and M. Agustina, “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.

Published
2023-06-11
How to Cite
[1]
N. Yahya, A. Fatmawati, N. Nurwan, and S. Nasib, “RAINBOW VERTEX-CONNECTION NUMBER ON COMB PRODUCT OPERATION OF CYCLE GRAPH (C_4) AND COMPLETE BIPARTITE GRAPH (K_(3,N))”, BAREKENG: J. Math. & App., vol. 17, no. 2, pp. 0673-0684, Jun. 2023.
Issue
Vol 17 No 2 (2023): BAREKENG: Journal of Mathematics and Its Applications
Section
Articles

Copyright (c) 2023 Nisky Imansyah Yahya, Ainun Fatmawati, Nurwan Nurwan, Salmun K Nasib

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