Computing The First Zagreb Index, The Wiener Index and The Gutman Index of The Power of Dihedral Group Using Python

bulqis nebulla syechah; Mutiara Aeqi Permata Prasetyo; Ni Luh Dewi Sintiari; Gede Adhitya Wisnu Wardhana

doi:10.20956/j.v22i1.44688

Authors

bulqis nebulla syechah Department Mathematics, Universitas Mataram
Mutiara Aeqi Permata Prasetyo Department Mathematics, Universitas Mataram
Ni Luh Dewi Sintiari Department of Informatics, Universitas Pendidikan Ganesha
Gede Adhitya Wisnu Wardhana Department Mathematics, Universitas Mataram

DOI:

https://doi.org/10.20956/j.v22i1.44688

Keywords:

Gutman Index, Python, Zagreb Index, Wiener Index

Abstract

This paper presents a computational study on three classical topological indices—the First Zagreb Index, Wiener Index, and Gutman Index—within the context of power graphs of the dihedral group , where is a positive integer representing half the order of the group. These indices are fundamental in mathematical chemistry and graph theory, serving as quantitative descriptors of graph structure and connectivity. The methodology involves constructing power graphs derived from and calculating the indices using Python programming, supported by the NetworkX, Matplotlib, and Gradio libraries. Numerical simulations were conducted for varying values of , revealing consistent algebraic patterns and insights into the structural complexity of the corresponding graphs. Additionally, an interactive Python-based interface is developed to facilitate real-time computation and visualization, thus promoting further exploration and application in algebraic graph theory

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