Inclusive Local Irregularity Vertex Coloring In Grid Graph Family
Abstract
Let is a simple graph and connected where is vertex set and is edge set. A maping as vertex k- labeling and function : is inclusive local irregularity vertex coloring, with . The minimum number of colors produced from inclusive local irregularity vertex coloring of graph is called inclusive chromatic number local irregularity, denoted by . On this paper, we learn about the inclusive local irregularity vertex coloring and determine the chromatic number on grid graph family.
Keywords
Full Text:
PDFReferences
Reinhard. Diestel, Graph theory. Springer. [2] G. Chartrand, C. Egan, and P. Zhang, “How to Label a Graph,” 2019. [Online]. Available: http://www.springer.com/series/10030 [3] Gary. Chartrand, P. Zhang, and Gary. Chartrand, A first course in graph theory. Dover Publications, 2012. [4] Aprilianto, B., Dafik, & Albirri, E. R. (2020). Dimensi Metrik Sisi pada Beberapa Graf Unicyclic. CGANT, 58-64. [5] S. Sudha, & K. Manikandan. (2015). General Pattern of Total Coloring of a Prism Graph of Layers and a Grid Graph. International Journal of Innovative Science and Modern Engineering (IJISME) ISSN: 2319-6386, Volume-3 Issue-3, 33-37. [6] Citra, S. M., A.I.Kristiana, & R.Adawiyah. (2021). Pewarnaan Packing pada Famili Graf Pohon dan Graf Hasil Operasi Amalgamasi Titik. Digital Repository Universitas Jember, 1-55. [7] M. I. Moussa, & E.M. Badr. (2016). Ladder and Subdivision of Ladder Graphs with Pendant Edges are Odd Graceful . International Journal on Applications of Graph Theory in Wireless Ad hoc Networks and Sensor Networks(GRAPH-HOC) Vol.8, No.1, 1-8. [8] Chartrand, G., & Zhang, P. (2009). Chromatic Graph Theory. USA : CRC Press, 1-483. [9] Akram, M., & Nawaz, S. (2015). Operations of Soft Graphs. Jurnal Science Direct, Vol.7, 423-449. [10] A. I. Kristiana, M. G. Halim, & R. Adawiyah. (2022). Pewarnaan Titik Ketakteraturan Lokal Inklusif pada Keluarga Graf Unicyclic. Contemporary Mathematics and Applications, Vol.4, No.1, 15-27. [11] O. Levin, Discrete mathematics : an open introduction, Third edition. 2019. [12] Balakrishnan R and Ranganathan K, “A Textbook of Graph Theory,” 2012. [Online]. Available: http://www.springer.com/series/223 [13] Yaqin, H. (2020). Pelabelan Titik dan Sisi L(2,1) pada Graf Sparkle. Central Library of Maulana Malik Ibrahim State Islamic University of Malang, 1-83. [14] A. Ma'arif, M. G. Halim, S. Indriani, A.I Kristiana, & R. Alfarisi. (2021). Pewarnaan Titik Ketakteraturan Lokal Inklusif pada Graf Kipas, Graf Petasan, dan Graf Matahari. Barekeng : Jurnal Ilmu Matematika dan Terapan, Vol.15, No.4, 727-734. [15] A. I. Kristiana, Dafik, R. Alfarisi, U. A. Anwar, and S. M. Citra, “An inclusive local irregularity coloring of graphs,” Advances in Mathematics: Scientific Journal, vol. 9, no. 10, pp. 8941–8946, 2020, doi: 10.37418/amsj.9.10.116. [16] Azahra, N., Dafik, & A.I.Kristiana. (2020). Pewarnaan Titik Ketakteraturan Lokal pada Graf Grid dan Keterkaitannya dengan Keterampilan Berpikir Tingkat Tinggi. Digital Repository Universitas Jember, 1-44. [17] Umilasari, R., Susilowati, L., Slamin Local irregularity chromatic number of vertex shackle product of graphs (Open Access) (2020) IOP Conference Series: Materials Science and Engineering, 821 (1), art. no. 012038. [18] Kristiana, A. I., Dafik, M. I. Utoyo, Alfarisi, R., Agustin, I. H., Venkatachalam, M. Local irregularity vertex coloring of graphs (2019) Int. J. Civil Eng. Technol, 10 (4), pp. 451-461. [19] Indah Kristiana, A., Utoyo, M.I., Dafik, Hesti Agustin, I., Alfarisi, R., Waluyo, E. On the chromatic number local irregularity of related wheel graph (Open Access) (2019) Journal of Physics: Conference Series, 1211 (1), art. no. 012003. [20] Kristiana, A.I., Alfarisi, R., Dafik, Azahra, N. Local irregular vertex coloring of some families graph (2022) Journal of Discrete Mathematical Sciences and Cryptography, 25 (1), pp. 15-30
DOI: https://doi.org/10.18860/ca.v9i1.20947
Refbacks
- There are currently no refbacks.
Copyright (c) 2024 Arika Indah Kristiana
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.