Bilangan Terhubung Titik Pelangi Kuat Graf Octa-Chain (OCm)

Nisky Imansyah Yahya; Karina Anselia Mamonto; Nurwan Nurwan; Lailany Yahya; Djihad Wungguli; La Ode Nashar

doi:10.34312/euler.v10i1.15177

Bilangan Terhubung Titik Pelangi Kuat Graf Octa-Chain (OCm)

Nisky Imansyah Yahya, Karina Anselia Mamonto, Nurwan Nurwan, Lailany Yahya, Djihad Wungguli, La Ode Nashar

Abstract

An Octa-Chain graph (OCm) is a graph formed by modifying the cycle graph C8 by adding an edge connecting the midpoints in C8. The minimum number of colors used to color the vertices in a graph so that every two vertices have a rainbow path is called the rainbow vertex-connected number denoted by rvc (G). While the minimum number of colors used to color the vertices in a graph so that every two vertices are always connected by a rainbow path is called a strong rainbow vertex connected number and is denoted by srvc (G). This study aims to determine the rainbow vertex-connected number (rvc) and the strong rainbow-vertex-connected number (srvc) in the Octa-Chain graph (OCm). The results obtained from this research are the rainbow vertex-connected number rvc (OCm)=2m and the strong rainbow-vertex-connected number srvc (OCm)=2m.

Keywords

Octa-Chain Graph; Rainbow Vertex-Connected Number; Strong Rainbow-Vertex-Connected Number

Full Text:

PDF

References

R. Munir, Matematika Diskrit, Bandung: Informatika, 2010.

I. K. Budayasa, Teori Graph dan Aplikasinya, Surabaya: UNESA University Press, 2007.

J. A. Gallian, "A Dynamic Survey Of Graph Labelling," Electronic Journal of Combinatorics, 2018.

M. Kubale, Graph Coloring, AMS Bookstore, 2004.

G. Chartrand, G. L. Johns, K. A. McKeon and P. Zhang, "Rainbow connection in graphs," Mathematica Bohemica, 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," Journal of Graph Theory, vol. 07, pp. 84-99, 2009.

X. Li, Y. Mao and Y. Shi, "The strong rainbow vertex connection of graphs," Utilitas Mathematica, vol. 93, pp. 213-223, 2014.

M. Afifuddin and I. K. Budayasa, "Bilangan Keterhubungan Titik Pelangi Kuat Pada Graf," MATH Unesa Jurnal Ilmiah Matematika, vol. 10, no. 1, pp. 33-40, 2022. doi: https://doi.org/10.26740/mathunesa.v10n1.p33-40

I. Lihawa, S. Ismail, I. K. Hasan, L. Yahya, S. K. Nasib and N. I. Yahya, "Bilangan Terhubung Titik Pelangi pada Graf Hasi lOperasi Korona Graf Prisma (Pm,2) dan Graf Lintasan," Jambura. J. Math., vol. 4, no. 1, pp. 145-151, 2022. doi: https://doi.org/10.34312/jjom.v4i1.11826

D. N. Simamora and A. Salman, "The Rainbow (Vertex) Connection Number of Pencil Graphs," Procedia Computer Science, vol. 74, pp. 138–142, 2015. doi: https://doi.org/10.1016/j.procs.2015.12.089

A. W. Bustan and A. Salman, "The Rainbow Vertex-Connection Number of Star Fan Graphs," CAUCHY–Jurnal Matematika Murni dan Aplikasi, vol. 5, no. 3, pp. 112-116, 2018. doi: https://doi.org/10.18860/ca.v5i3.5516

A. F. Akadji, M. R. Katili, S. K. Nasib and N. I. Yahya, "Rainbow vertex connection number and strong rainbow vertex connection number on slinky graph (SlnC4)," DESIMAL: Jurnal Matematika, vol. 4, pp. 123-132, 2021.doi: https://doi.org/10.24042/djm.v4i2.7276

R. Diestel, Graph Theory 4th Edition, Springer, 2010.

DOI: https://doi.org/10.34312/euler.v10i1.15177