Hyper-Wiener and Szeged Indices of non-Coprime Graphs of Modulo Integer Groups

Lalu Hasan Ghoffari; I Gede Adhitya Wisnu Wardhana; Putu Kartika Dewi; I Nengah Suparta

doi:10.29303/emj.v8i1.244

Authors

Lalu Hasan Ghoffari Department of Mathematics, Universitas Mataram, Indonesia
I Gede Adhitya Wisnu Wardhana Department of Mathematics, Universitas Mataram, Indonesia
Putu Kartika Dewi Department of Mathematics, Universitas Pendidikan Ganesha, Indonesia
I Nengah Suparta Department of Mathematics, Universitas Pendidikan Ganesha, Indonesia

DOI:

https://doi.org/10.29303/emj.v8i1.244

Keywords:

non-Coprime Graph, Hyper-Wiener Index, Szeged Index

Abstract

The non-coprime graph of the integer modulo group is a graph whose vertices represent the elements of the integer modulo group, excluding the identity element. Two distinct vertices are adjacent if and only if their orders are not relatively prime. This study explores two topological indices, the Hyper-Wiener index and the Szeged index, in the non-coprime graph of the integer modulo-n group. The results reveal that these indices are equal when the order is a prime power but differ when the order is the product of two distinct prime numbers. This research provides new insights into the patterns and characteristics of these indices, contributing to a broader understanding of the application of graph theory to abstract group structures.

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