Degree-based topological indices of the idempotent graph of the ring Zn

Let R be a finite commutative ring with a non-zero identity, and Id(R) be the set of idempotent elements of R. The idempotent graph of R, denoted by GId(R), is a simple undirected graph with all elements of R as vertices, and two distinct vertices u, v are adjacent if and only if u+v∈Id(R). In this...

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Main Authors: Osman Gani Mondal, Sk. Md. Abu Nayeem
Format: Article
Language:English
Published: Elsevier 2024-12-01
Series:Examples and Counterexamples
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Online Access:http://www.sciencedirect.com/science/article/pii/S2666657X24000272
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author Osman Gani Mondal
Sk. Md. Abu Nayeem
author_facet Osman Gani Mondal
Sk. Md. Abu Nayeem
author_sort Osman Gani Mondal
collection DOAJ
description Let R be a finite commutative ring with a non-zero identity, and Id(R) be the set of idempotent elements of R. The idempotent graph of R, denoted by GId(R), is a simple undirected graph with all elements of R as vertices, and two distinct vertices u, v are adjacent if and only if u+v∈Id(R). In this paper, we consider the idempotent graph of the ring Zn and investigate some degree-based topological indices, such as the general sum-connectivity index, the general Randić index, the general Zagreb index, and the Sombor index of that graph by considering the M-polynomial of the graph.
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spelling doaj-art-03ffbe395a2844faacfd7d4f65e583f52025-08-20T02:34:53ZengElsevierExamples and Counterexamples2666-657X2024-12-01610016110.1016/j.exco.2024.100161Degree-based topological indices of the idempotent graph of the ring ZnOsman Gani Mondal0Sk. Md. Abu Nayeem1Department of Mathematics and Statistics, Aliah University, Kolkata 700 160, IndiaCorresponding author.; Department of Mathematics and Statistics, Aliah University, Kolkata 700 160, IndiaLet R be a finite commutative ring with a non-zero identity, and Id(R) be the set of idempotent elements of R. The idempotent graph of R, denoted by GId(R), is a simple undirected graph with all elements of R as vertices, and two distinct vertices u, v are adjacent if and only if u+v∈Id(R). In this paper, we consider the idempotent graph of the ring Zn and investigate some degree-based topological indices, such as the general sum-connectivity index, the general Randić index, the general Zagreb index, and the Sombor index of that graph by considering the M-polynomial of the graph.http://www.sciencedirect.com/science/article/pii/S2666657X24000272Idempotent graphRandić indexZagreb indexSum-connectivity indexSombor index
spellingShingle Osman Gani Mondal
Sk. Md. Abu Nayeem
Degree-based topological indices of the idempotent graph of the ring Zn
Examples and Counterexamples
Idempotent graph
Randić index
Zagreb index
Sum-connectivity index
Sombor index
title Degree-based topological indices of the idempotent graph of the ring Zn
title_full Degree-based topological indices of the idempotent graph of the ring Zn
title_fullStr Degree-based topological indices of the idempotent graph of the ring Zn
title_full_unstemmed Degree-based topological indices of the idempotent graph of the ring Zn
title_short Degree-based topological indices of the idempotent graph of the ring Zn
title_sort degree based topological indices of the idempotent graph of the ring zn
topic Idempotent graph
Randić index
Zagreb index
Sum-connectivity index
Sombor index
url http://www.sciencedirect.com/science/article/pii/S2666657X24000272
work_keys_str_mv AT osmanganimondal degreebasedtopologicalindicesoftheidempotentgraphoftheringzn
AT skmdabunayeem degreebasedtopologicalindicesoftheidempotentgraphoftheringzn