PEWARNAAN TITIK TOTAL SUPER ANTI-AJAIB LOKAL PADA GRAF PETERSEN DIPERUMUM P(n,k) DENGAN k=1,2

  • Deddy Setyawan Universitas Jember
  • Anis Nur Afni Universitas Jember
  • Rafiantika Megahnia Prihandini Universitas Jember
  • Ermita Rizki Albirri Universitas Jember
  • Arika Indah Kristiana Universitas Jember
DOI: https://doi.org/10.30598/barekengvol15iss4pp651-658
Keywords: Vertex coloring, Generalized Petersen Graph, local super antimagic total chromatic number

Abstract

The local antimagic total vertex labeling of graph G is a labeling that every vertices and edges label by natural number from 1 to  such that every two adjacent vertices has different weights, where is The sum of a vertex label and the labels of all edges that incident to the vertex. If the labeling start the smallest label from the vertex  then the edge  so that kind of coloring is called the local super antimagic total vertex labeling. That local super antimagic total vertex labeling induces vertex coloring of graph G where for vertex v, the weight  w(v) is the color of  v. The minimum number of colors that obtained by coloring that induces by local super antimagic total vertex labeling of G called the chromatic number of local super antimagic total vertex coloring of G, denoted by χlsat(G). In this paper, we consider the chromatic number of local super antimagic total vertex coloring of Generalized Petersen Graph P(n,k) for k=1, 2.

Downloads

Download data is not yet available.

References

S. Arumugam, K. Premalatha, M. Bača, and A. Semaničová-Feňovčíková, “Local Antimagic Vertex Coloring of a Graph,” Graphs Comb., vol. 33, no. 2, pp. 275–285, 2017, doi: 10.1007/s00373-017-1758-7.

F. F. Hadiputra, D. R. Silaban, and T. K. Maryati, “Super local edge anti-magic total coloring of paths and its derivation,” Indones. J. Comb., vol. 3, no. 2, p. 126, 2020, doi: 10.19184/ijc.2019.3.2.6.

D. F. Putri, D. Dafik, I. H. Agustin, and R. Alfarisi, “On the local vertex antimagic total coloring of some families tree,” J. Phys. Conf. Ser., vol. 1008, no. 1, 2018, doi: 10.1088/1742-6596/1008/1/012035.

S. Slamin, N. O. Adiwijaya, M. A. Hasan, D. Dafik, and K. Wijaya, “Local super antimagic total labeling for vertex coloring of graphs,” Symmetry (Basel)., vol. 12, no. 11, pp. 1–17, 2020, doi: 10.3390/sym12111843.

S. A. Pratama, S. Setiawani, and Slamin, “Local super antimagic total vertex coloring of some wheel related graphs,” J. Phys. Conf. Ser., vol. 1538, no. 1, 2020, doi: 10.1088/1742-6596/1538/1/012014.

V. Yegnanarayanan, “On some aspects of the generalized Petersen graph,” Electron. J. Graph Theory Appl., vol. 5, no. 2, pp. 163–178, 2017, doi: 10.5614/ejgta.2017.5.2.1.

K. Premalatha, S. Arumugam, Y. C. Lee, and T. M. Wang, “Local antimagic chromatic number of trees - I,” J. Discret. Math. Sci. Cryptogr., 2020, doi: 10.1080/09720529.2020.1772985.

E. Y. Kurniawati, I. H. Agustin, D. Dafik, R. Alfarisi, and M. Marsidi, “On the local antimagic total edge chromatic number of amalgamation of graphs,” AIP Conf. Proc., vol. 2014, no. September, 2018, doi: 10.1063/1.5054494.

N. H. Nazula, S. Slamin, and D. Dafik, “Local antimagic vertex coloring of unicyclic graphs,” Indones. J. Comb., vol. 2, no. 1, p. 30, 2018, doi: 10.19184/ijc.2018.2.1.4.

I. H. Agustin, M. Hasan, D. Dafik, R. Alfarisi, A. I. Kristiana, and R. M. Prihandini, “Local Edge Antimagic Coloring of Comb Product of Graphs,” J. Phys. Conf. Ser., vol. 1008, no. 1, 2018, doi: 10.1088/1742-6596/1008/1/012038.

Dafik, I. H. Agustin, Marsidi, and E. Y. Kurniawati, “On the local antimagic vertex coloring of sub-devided some special graph,” J. Phys. Conf. Ser., vol. 1538, no. 1, 2020, doi: 10.1088/1742-6596/1538/1/012021.

R. Alfarisi, Dafik, R. Adawiyah, R. M. Prihandini, E. R. Albirri, and I. H. Agustin, “On the partition dimension of edge corona product of path and cycle,” J. Phys. Conf. Ser., vol. 1211, no. 1, pp. 40–48, 2019, doi: 10.1088/1742-6596/1211/1/012014.

I. H. Agustin, M. Hasan, Dafik, R. Alfarisi, and R. M. Prihandini, “Local edge antimagic coloring of graphs,” Far East J. Math. Sci., vol. 102, no. 9, pp. 1925–1941, 2017, doi: 10.17654/MS102091925.

M. E. Watkins, “A theorem on tait colorings with an application to the generalized Petersen graphs,” J. Comb. Theory, vol. 6, no. 2, pp. 152–164, 1969, doi: 10.1016/S0021-9800(69)80116-X.

S. Arumugam, Y.-C. Lee, K. Premalatha, and T.-M. Wang, “On Local Antimagic Vertex Coloring for Corona Products of Graphs,” pp. 1–29, 2018, [Online]. Available: http://arxiv.org/abs/1808.04956.

Published
2021-12-01
How to Cite
[1]
D. Setyawan, A. Afni, R. Prihandini, E. Albirri, and A. Kristiana, “PEWARNAAN TITIK TOTAL SUPER ANTI-AJAIB LOKAL PADA GRAF PETERSEN DIPERUMUM P(n,k) DENGAN k=1,2”, BAREKENG: J. Math. & App., vol. 15, no. 4, pp. 651-658, Dec. 2021.
Issue
Vol 15 No 4 (2021): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Section
Articles

Authors who publish with this Journal agree to the following terms:

  1. Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
  2. Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
  3. Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.