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2024 | OriginalPaper | Chapter

Analysis of Some Topological Indices Over the Weakly Zero-Divisor Graph of the Ring \(\mathbb {Z}_p \times \mathbb {Z}_q \times \mathbb {Z}_r\)

Authors : Nadeem ur Rehman, Shabir Ahmad Mir, Mohd Nazim

Published in: Advances in Ring Theory and Applications

Publisher: Springer Nature Switzerland

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Abstract

In this paper, we study some basic properties of weakly zero-divisor graph of the ring \(\mathbb {Z}_p \times \mathbb {Z}_q \times \mathbb {Z}_r\), denoted by \(\text {W}{\Gamma }(\mathbb {Z}_p \times \mathbb {Z}_q \times \mathbb {Z}_r)\), where p, q and r are prime numbers greater than 2 and not necessarily distinct. Further, we discuss Wiener index, Gutman index, first K Banhatti index, second K Banhatti index, Forgotten topological index, Forgotten topological coindex, and degree distance index of \(\text {W}{\Gamma }(\mathbb {Z}_p \times \mathbb {Z}_q \times \mathbb {Z}_r)\).

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previous chapter A Note on -Generalized Skew Derivations on Prime Rings

next chapter A Study of Central Identities Equipped with Skew Lie Product Involving Generalized Derivations

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Title: Analysis of Some Topological Indices Over the Weakly Zero-Divisor Graph of the Ring
Authors: Nadeem ur Rehman
Shabir Ahmad Mir
Mohd Nazim
Publisher: Springer Nature Switzerland
Book: Advances in Ring Theory and Applications
Print ISBN: 978-3-031-50794-6

Electronic ISBN: 978-3-031-50795-3

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-50795-3_8

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