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Open AccessArticle
Exploring Ring Structures: Multiset Dimension Analysis in Compressed Zero-Divisor Graphs
by
Nasir Ali
Nasir Ali
Nasir Ali is currently working as a lecturer of mathematics at the COMSATS University Islamabad, He [...]
Nasir Ali is currently working as a lecturer of mathematics at the COMSATS University Islamabad, Vehari Campus. He is a Ph.D. scholar at the COMSATS University Islamabad, Lahore Campus. From 2018 to 2023, he served as a visiting lecturer in mathematics at the University of Education, Vehari Campus. His area of research is graph theory, algebraic structures, pure mathematics, algebra, and metric parameters. Moreover, he also worked as a lecturer of mathematics at the Govt. Postgraduate college Vehari.
1
,
Hafiz Muhammad Afzal Siddiqui
Hafiz Muhammad Afzal Siddiqui 1
,
Muhammad Imran Qureshi
Muhammad Imran Qureshi 2
,
Suhad Ali Osman Abdallah
Suhad Ali Osman Abdallah 3,
Albandary Almahri
Albandary Almahri 4,
Jihad Asad
Jihad Asad 5,*
and
Ali Akgül
Ali Akgül 6,7,*
1
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
2
Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61100, Pakistan
3
Applied College, King Khalid University, Khamis Mushait 61421, Saudi Arabia
4
Department of Chemistry, College of Science and Humanities in Al-Kharj, Al-Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
5
Department of Physics, Faculty of Applied Science, Palestine Technical University-Kadoorie, Tulkarm P305, Palestine
6
Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, Mersin10, 99138 Nicosia, Turkey
7
Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, Turkey
*
Authors to whom correspondence should be addressed.
Symmetry 2024, 16(7), 930; https://doi.org/10.3390/sym16070930 (registering DOI)
Submission received: 14 May 2024
/
Revised: 29 May 2024
/
Accepted: 3 June 2024
/
Published: 20 July 2024
Abstract
:
This paper explores the concept of multiset dimensions (Mdim) of compressed zero-divisor graphs (CZDGs) associated with rings. The authors investigate the interplay between the ring-theoretic properties of a ring and the associated compressed zero-divisor graph. An undirected graph consisting of a vertex set , where and is called a compressed zero-divisor graph, denoted by . An edge is formed between two vertices and of if and only if that is, iff . For a ring , graph is said to be realizable as if is isomorphic to . We classify the rings based on Mdim of their associated CZDGs and obtain the bounds for the Mdim of the compressed zero-divisor graphs. We also study the Mdim of realizable graphs of rings. Moreover, some examples are provided to support our results. Notably, we discuss the interconnection between Mdim, girth, and diameter of CZDGs, elucidating their symmetrical significance.
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© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
MDPI and ACS Style
Ali, N.; Siddiqui, H.M.A.; Qureshi, M.I.; Abdallah, S.A.O.; Almahri, A.; Asad, J.; Akgül, A.
Exploring Ring Structures: Multiset Dimension Analysis in Compressed Zero-Divisor Graphs. Symmetry 2024, 16, 930.
https://doi.org/10.3390/sym16070930
AMA Style
Ali N, Siddiqui HMA, Qureshi MI, Abdallah SAO, Almahri A, Asad J, Akgül A.
Exploring Ring Structures: Multiset Dimension Analysis in Compressed Zero-Divisor Graphs. Symmetry. 2024; 16(7):930.
https://doi.org/10.3390/sym16070930
Chicago/Turabian Style
Ali, Nasir, Hafiz Muhammad Afzal Siddiqui, Muhammad Imran Qureshi, Suhad Ali Osman Abdallah, Albandary Almahri, Jihad Asad, and Ali Akgül.
2024. "Exploring Ring Structures: Multiset Dimension Analysis in Compressed Zero-Divisor Graphs" Symmetry 16, no. 7: 930.
https://doi.org/10.3390/sym16070930
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