Indeks Harary Graf Koprima dan Graf Pangkat pada Grup Bilangan Bulat Modulo serta Grup Dihedral

Luzianawati Luzianawati; Rio Satriyantara

doi:10.29303/semeton.v2i2.307

Authors

Luzianawati Luzianawati Program Studi Matematika, Universitas Mataram
Rio Satriyantara Program Studi Matematika, Universitas Mataram

DOI:

https://doi.org/10.29303/semeton.v2i2.307

Keywords:

Harary Index, Coprime Graph, Power Graph, Modulo Group, Dihedral Group

Abstract

This study investigates the Harary Index of coprime graphs and power graphs constructed from the integer modulo group and the dihedral group. A coprime graph is defined as a graph whose vertices represent the elements of a group, where two vertices are adjacent if the orders of the corresponding elements are relatively prime. Meanwhile, a power graph is a graph in which two elements are connected whenever one is a power of the other within the group. The Harary Index is employed to measure the topological characteristics of the graph based on the distances between its vertices. The results show that the structure of the generated graphs allows for an explicit computation of the Harary Index, particularly for groups whose orders are prime powers.graphs facilitate the calculation of the Harary Index , especially for groups with prime power order.

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