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2024 | OriginalPaper | Chapter

The Wiener Index, the Harmonic Index, and the Graph Representation of the Prime Ideal Graph for the Integers Modulo Rings with Prime Power Order

Authors : Hindani Kusuma Ningrum, Evi Yuniartika Asmarani, I Gede Adhitya Wisnu Wardhana, Salwa, Zata Yumni Awanis

Published in: Applied and Computational Mathematics

Publisher: Springer Nature Singapore

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Abstract

The Wiener index and the Harmonic index of a graph are significant metrics in the realm of graph theory, offering valuable perspectives on the graph's structure, characteristics, and behavior. This research aims to determine the form of the representation of prime ideal graphs in the modulo integer ring with prime power order, and its topological indices such as the Wiener index and the Harmonic index. The graph is empty when the order is prime, and the graph contains complete subgraph and star subgraph when the order is prime power. Next, we can find the Weiner index and the Harmonic index of the graph. With the help of the complete subgraph and star subgraph mentioned earlier, we can find the Wiener index and the Harmonic index of the graph.

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previous chapter On Conformable Fractional Riesz Bounded Variation of Order
next chapter Multiplicative Sum Nano Zagreb Index of Various 2-Power Corona Graphs
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Metadata
Title
The Wiener Index, the Harmonic Index, and the Graph Representation of the Prime Ideal Graph for the Integers Modulo Rings with Prime Power Order
Authors
Hindani Kusuma Ningrum
Evi Yuniartika Asmarani
I Gede Adhitya Wisnu Wardhana
Salwa
Zata Yumni Awanis
Copyright Year
2024
Publisher
Springer Nature Singapore
Book
Applied and Computational Mathematics

Print ISBN: 978-981-9721-35-1

Electronic ISBN: 978-981-9721-36-8

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-981-97-2136-8_28

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