AN INCLUSIVE LOCAL IRREGULARITY VERTEX COLORING OF BOOK GRAPH FAMILY

  • Robiatul Adawiyah Mathematics Education, Faculty of Teacher Training and Education, University of Jember, Indonesia
  • Muslihatul Aima Mathematics Education, Faculty of Teacher Training and Education, University of Jember, Indonesia
  • Arika Indah Kristiana Mathematics Education, Faculty of Teacher Training and Education, University of Jember, Indonesia
DOI: https://doi.org/10.30598/barekengvol17iss2pp0601-0608
Keywords: An inclusive local irregularity vertex coloring, book graphs

Abstract

Let  is a simple and connected graph with    as vertex set and  as edge set. Vertex labeling on inclusive local irregularity vertex coloring is defined by mapping and the function of the inclusive local irregularity vertex coloring is with . In other words, an inclusive local irregularity vertex coloring is defined by coloring the graph so that its weight value is obtained by adding up the labels of the neighboring vertex and its label. The inclusive local irregularity chromatic number is defined as the minimum number of colors obtained from coloring the vertex of the inclusive local irregularity in graph G, denoted by . In this paper, we learn about the inclusive local irregularity vertex coloring and determine the chromatic number on the book graphs.

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References

Slamin, Teori Graf dan Aplikasinya. Jember: CV. Dream Litral Buana, 2019.

G. Z. Chartrand, A first course in graph theory. Dover Publications, 2012.

K. A. N Azahra, “On the Local Irregularity Vertex ,” International Journal of Academic and Applied Research, pp. 1–4, 2020.

Dafik, Teori Graf, Aplikasi dan Tumbuhnya Keterampilan Berpikir Tingkat Tinggi. Pidato Pengukuhan Guru Besar. Jember: Pidato Ilmiah Pengukuhan Profesor di Lingkungan UNEJ. Mei., 2015.

P. Zhang, A Kaleidoscopic View of Graph Colorings. USA: Springer Nature, 2016.

E. Sudirman, Pewarnaan Simpul Graf Menggunakan Algoritma WelchPowell dan Aplikasinya pada Penjadwalan Kuliah di Jurusan Matematika FMIPA UNM . Makassar: Universitas Negeri Makassar, 2013.

M. d Mahmudah, Rainbow Connection hasil operasi graf. Jember: Unversitas Jember, 2014.

Kristiana. A. I, Dafik, R.Alfarisi, U. A. Anwar, and S. M. Citra, “An Inclusive Lokal Irregularity Coloring of Graphs,” Advances in Mathematics: Scientific Journal, vol. 10, pp. 9841–9846, 2020.

U. A. Anwar, “Pewarnaan Ketakteraturan Lokal Inklusif pada Keluarga Graf Pohon Tree,” CCGANT JMA, vol. 2, no. 1, 2021.

A. H. Ma’arif, “Pewarnaan Titik Ketakteraturan Lokal Inklusif pada Graf Kipas, Graf Petasan, dan Graf Matahari,” BAREKENG: Jurnal Ilmu Matematika Dan Terapan, vol. 4, no. 1, pp. 15–27, 2021.

H. M. Kristiana. A. I., “Pewarnaan Titik Ketakteraturan Lokal Inklusif pada Keluarga Graf Unicyclic,” Contemporary Mathematics and Applications, vol. 4, no. 1, pp. 15–27, 2022.

S. I. Kristiana. A. I., “Pewarnaan Titik Ketakteraturan Lokal Inklusif pada pada Hasil Operasi Comb Graf Bintang,” Contemporary Mathematics and Applications, vol. 4, no. 1, pp. 1–14, 2022.

L. D. Minarti, Dafik, S. Setiawani, Slamin, and A. Fatahillah, “Pewarnaan Sisi Dinamis pada Graf Hasil Operasi Amalgamasi Titik Keluarga Graf Pohon dan Kaitannya Dengan Keterampilan Berpikir Tingkat Tinggi,” Paper Knowledge. Toward a Media History of Documents, pp. 15–22, 2019.

Z. Y. Awanis, A. Salman, A. W. Saputro, M. Baca, and A. S. Fenovcikova, “The strong 3-rainbow index of edge-amalgamation of some graphs,” Turkish Journal of Mathematics, vol. 44, pp. 446–462, 2020.

Kristiana.A.I., Dafik, Agustin I. h, Utoyo, R.Alfarisi, and Waluyo E, On The Chromatic Number Local Irregularity of Related Wheel Graph. IOP Conf. Series : Journal of Physics. Conf. Series. 1211.0120003, 2019.

Published
2023-06-11
How to Cite
[1]
R. Adawiyah, M. Aima, and A. Kristiana, “AN INCLUSIVE LOCAL IRREGULARITY VERTEX COLORING OF BOOK GRAPH FAMILY”, BAREKENG: J. Math. & App., vol. 17, no. 2, pp. 0601-0608, Jun. 2023.
Issue
Vol 17 No 2 (2023): BAREKENG: Journal of Mathematics and Its Applications
Section
Articles

Copyright (c) 2023 Robiatul Adawiyah, Muslihatul Aima, Arika Indah Kristiana

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