# 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
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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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.
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Articles