Original Research Article

Article volume = 2023 and issue = 1

Pages: 90–95

Article publication Date: July 30, 2023

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# A Note on the Harmonic and Gutman Index of Coprime Graph of the Group of Integers Modulo Prime Power

#### John Rafael M. Antalan

Department of Mathematics and Physics, College of Science, Central Luzon State University (3120), Science City of Munoz, Nueva Ecija, Philippines.

##### Abstract:

In a recent paper by M.N. Husni and his colleagues, they were able to determine the harmonic and Gutman index of the coprime graph of the group of integers modulo prime power. In this research note, we give a short proof of their results using some well-known results on the harmonic and Gutman index of a graph. Moreover, we give a general version of their result using a well-known result on group isomorphism in group theory.

##### Keywords:

Harmonic index, Gutman Index, Coprime Graph, Group of integers modulo n.

##### References:

- [1] M. N. Husni, H. Syafitri, A. M. Siboro, A. G. Syarifudin, Q. Aini, and I G. A. W. Wardhana The harmonic and the Gutman index of coprime graph of integer group modulo with order prime power, J. Math. & App., 16(3) (2022),961–966. 1, 2.1, 3
- [2] 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), 3(1 (2020),15–18. 1
- [3] J. B. Fraleigh, A first course in abstract algebra, 7th Ed., Addison-Wesley, Boston, (2003). 2.1
- [4] J. A. Gallian, Contemporary abstract algebra, 9th Ed., Cengage Learning, Boston, (2017). 2.1
- [5] L. Zhong The harmonic index of graphs, Appl. Math. Lett., 25(2012) (2012),561–566. 2.1, 3
- [6] V. Andova, D. Dimitrov, J. Fink, and R. Skrekovski Bounds on Gutman index, MATCH Commun. Math. Comput. Chem., 67(2012) (2012),515–524. 2.1, 3

##### Cite this article as:

- John Rafael M. Antalan, A Note on the Harmonic and Gutman Index of Coprime Graph of the Group of Integers Modulo Prime Power, Communications in Combinatorics, Cryptography & Computer Science, 2023(1), PP.90–95, 2023
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