THE HARMONIC INDEX AND THE GUTMAN INDEX OF COPRIME GRAPH OF INTEGER GROUP MODULO WITH ORDER OF PRIME POWER

  • Muhammad Naoval Husni Department of Mathematics, Faculty of Mathematics and Natural Sciences, Mataram University, Nusa Tenggara Barat, Indonesia
  • Hanna Syafitri Department of Mathematics, Faculty of Mathematics and Natural Sciences, Mataram University, Nusa Tenggara Barat, Indonesia
  • Ayes Malona Siboro Department of Mathematics, Faculty of Mathematics and Natural Sciences, Mataram University, Nusa Tenggara Barat, Indonesia
  • Abdul Gazir Syarifudin Department of Magister Mathematics, Faculty of Mathematics and Natural Sciences, Institut of Technology Bandung, Jawa Barat, Indonesia.
  • Qurratul Aini Department of Mathematics, Faculty of Mathematics and Natural Sciences, Mataram University, Nusa Tenggara Barat, Indonesia
  • I Gede Adhitya Wisnu Wardhana Department of Mathematics, Faculty of Mathematics and Natural Sciences, Mataram University, Nusa Tenggara Barat, Indonesia
DOI: https://doi.org/10.30598/barekengvol16iss3pp961-966
Keywords: Harmonic Index, Gutman Index, Coprime Graph, Integer Group Modulo

Abstract

In the field of mathematics, there are many branches of study, especially in graph theory, mathematically a graph is a pair of sets, which consists of a non-empty set whose members are called vertices and a set of distinct unordered pairs called edges. One example of a graph from a group is a coprime graph, where a coprime graph is defined as a graph whose vertices are members of a group and two vertices with different x and y are neighbors if only if (|x|,|y|)=1. In this study, the author discusses the Harmonic Index and Gutman Index of Coprime Graph of Integer Group Modulo n. The method used in this research is a literature review and analysis based on patterns formed from several case studies for the value of n. The results obtained from this study are the coprime graph of the group of integers modulo n has the harmonic index of  and the Gutman index  for  where  is prime and  is a natural number.

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References

A. G. Syarifudin, Nurhabibah, D. P. Malik, and I. G. A. W. dan Wardhana, “Some characterizatsion of coprime graph of dihedral group D2n,” Journal of Physics: Conference Series, vol. 1722, no. 1, 2021, doi: 10.1088/1742-6596/1722/1/012051.

N. Nurhabibah, A. G. Syarifudin, and I. G. A. W. Wardhana, “Some Results of The Coprime Graph of a Generalized Quaternion Group Q_4n,” InPrime: Indonesian Journal of Pure and Applied Mathematics, vol. 3, no. 1, pp. 29–33, 2021, doi: 10.15408/inprime.v3i1.19670.

A. Gazir and I. G. A. W. Wardhana, “Subgrup Non Trivial Dari Grup Dihedral,” Eigen Mathematics Journal, vol. 1, no. 2, p. 73, Dec. 2019, doi: 10.29303/emj.v1i2.26.

X. Ma, H. Wei, and L. Yang, “The Coprime graph of a group,” International Journal of Group Theory, vol. 3, no. 3, pp. 13–23, 2014, doi: 10.22108/ijgt.2014.4363.

F. Mansoori, A. Erfanian, and B. Tolue, “Non-coprime graph of a finite group,” AIP Conference Proceedings, vol. 1750, no. June 2016, 2016, doi: 10.1063/1.4954605.

M. Masriani, R. Juliana, A. G. Syarifudin, I. G. A. W. Wardhana, I. Irwansyah, and N. W. Switrayni, “Some Result Of Non-Coprime Graph Of Integers Modulo N Group For N A Prime Power,” Journal of Fundamental Mathematics and Applications (JFMA), vol. 3, no. 2, pp. 107–111, 2020, doi: 10.14710/jfma.v3i2.8713.

W. U. Misuki, I. G. A. W. Wardhana, N. W. Switrayni, and Irwansyah, “Some results of non-coprime graph of the dihedral group D2n for n a prime power,” AIP Conference Proceedings, vol. 2329, no. February, 2021, doi: 10.1063/5.0042587.

E. Y. Asmarani, A. G. Syarifudin, G. Adhitya, W. Wardhana, and W. Switrayni, “Eigen Mathematics Journal The Power Graph of a Dihedral Group,” vol. 4, no. 2, 2021, doi: 10.29303/emj.v4i2.117.

T. Chelvam and M. Sattanathan, “Power graph of finite abelian groups,” Algebra and Discrete Mathematics, vol. 16, no. 1, pp. 33–41, 2013.

N. Nurhabibah, A. Gazir Syarifudin, I. Gede Adhitya Wisnu Wardhana, and Q. Aini, “Eigen Mathematics Journal The Intersection Graph of a Dihedral Group,” vol. 4, no. 2, 2021, doi: 10.29303/emj.v4i2.119.

R. Juliana, M. Masriani, I. G. A. W. Wardhana, N. W. Switrayni, and I. Irwansyah, “Coprime Graph Of Integers Modulo N Group And Its Subgroups,” Journal of Fundamental Mathematics and Applications (JFMA), vol. 3, no. 1, pp. 15–18, 2020, doi: 10.14710/jfma.v3i1.7412.

H. Hua, K. C. Das, and H. Wang, “On atom-bond connectivity index of graphs,” Journal of Mathematical Analysis and Applications, vol. 479, no. 1, pp. 1099–1114, Nov. 2019, doi: 10.1016/j.jmaa.2019.06.069.

A. G. Syarifudin, I. G. A. W. Wardhana, N. W. Switrayni, and Q. Aini, “The Clique Numbers and Chromatic Numbers of The Coprime Graph of a Dihedral Group,” IOP Conference Series: Materials Science and Engineering, vol. 1115, no. 1, p. 012083, 2021, doi: 10.1088/1757-899x/1115/1/012083.

M. Javaid, M. K. Siddique, and E. Bonyah, “Computing Gutman Connection Index of Thorn Graphs,” Journal of Mathematics, vol. 2021, 2021, doi: 10.1155/2021/2289514.

L. Zhong, “The harmonic index for graphs,” Applied Mathematics Letters, vol. 25, no. 3, pp. 561–566, Mar. 2012, doi: 10.1016/j.aml.2011.09.059.

Published
2022-09-01
How to Cite
[1]
M. Husni, H. Syafitri, A. Siboro, A. Syarifudin, Q. Aini, and I. G. A. Wardhana, “THE HARMONIC INDEX AND THE GUTMAN INDEX OF COPRIME GRAPH OF INTEGER GROUP MODULO WITH ORDER OF PRIME POWER”, BAREKENG: J. Math. & App., vol. 16, no. 3, pp. 961-966, Sep. 2022.
Issue
Vol 16 No 3 (2022): BAREKENG: Journal of Mathematics and Its Applications
Section
Articles

Copyright (c) 2022 Muhammad Naoval Husni, Hanna Syafitri, Ayes Malona Siboro, Abdul Gazir Syarifudin, Qurratul Aini, I Gede Adhitya Wisnu Wardhana

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