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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Elsevier
2024-12-01
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| 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. |
| format | Article |
| id | doaj-art-03ffbe395a2844faacfd7d4f65e583f5 |
| institution | OA Journals |
| issn | 2666-657X |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Examples and Counterexamples |
| 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 |