On subgroups product graph of finite groups
This paper explores Subgroup Product Graphs (SPG) in cyclic groups, presenting a Vertex Degrees Formula based on the prime factorization of a positive integer n. The Isolated Vertex Property asserts that for a positive integer n, the SPG γ_sp(G) lacks isolated vertices. The Matrix Degree and Edge Fo...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2024-01-01
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| Series: | BIO Web of Conferences |
| Online Access: | https://www.bio-conferences.org/articles/bioconf/pdf/2024/16/bioconf_iscku2024_00155.pdf |
| _version_ | 1797213233706172416 |
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| author | Abd Shakir Jawad Shelash Hayder B. |
| author_facet | Abd Shakir Jawad Shelash Hayder B. |
| author_sort | Abd Shakir Jawad |
| collection | DOAJ |
| description | This paper explores Subgroup Product Graphs (SPG) in cyclic groups, presenting a Vertex Degrees Formula based on the prime factorization of a positive integer n. The Isolated Vertex Property asserts that for a positive integer n, the SPG γ_sp(G) lacks isolated vertices. The Matrix Degree and Edge Formula provide a matrix representation and calculate the edges in SPG. Additionally, a Subgraph Relation identifies the complete graph Kπ(n) as a subgraph in γ_sp(G). Specific Examples illustrate vertex degrees for different n values. In essence, the study contributes isomorphisms, characterizes properties, and computes degrees and edges for diverse subgroups in Subgroup Product Graphs. |
| first_indexed | 2024-04-24T10:55:02Z |
| format | Article |
| id | doaj.art-2274a4e8737d43d585bb1cedc3a7c1c7 |
| institution | Directory Open Access Journal |
| issn | 2117-4458 |
| language | English |
| last_indexed | 2024-04-24T10:55:02Z |
| publishDate | 2024-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | BIO Web of Conferences |
| spelling | doaj.art-2274a4e8737d43d585bb1cedc3a7c1c72024-04-12T07:36:29ZengEDP SciencesBIO Web of Conferences2117-44582024-01-01970015510.1051/bioconf/20249700155bioconf_iscku2024_00155On subgroups product graph of finite groupsAbd Shakir Jawad0Shelash Hayder B.1Departement of Mathematics, Faculty of Computer Sciences and Mathematics, University of KufaDepartement of Mathematics, Faculty of Computer Sciences and Mathematics, University of KufaThis paper explores Subgroup Product Graphs (SPG) in cyclic groups, presenting a Vertex Degrees Formula based on the prime factorization of a positive integer n. The Isolated Vertex Property asserts that for a positive integer n, the SPG γ_sp(G) lacks isolated vertices. The Matrix Degree and Edge Formula provide a matrix representation and calculate the edges in SPG. Additionally, a Subgraph Relation identifies the complete graph Kπ(n) as a subgraph in γ_sp(G). Specific Examples illustrate vertex degrees for different n values. In essence, the study contributes isomorphisms, characterizes properties, and computes degrees and edges for diverse subgroups in Subgroup Product Graphs.https://www.bio-conferences.org/articles/bioconf/pdf/2024/16/bioconf_iscku2024_00155.pdf |
| spellingShingle | Abd Shakir Jawad Shelash Hayder B. On subgroups product graph of finite groups BIO Web of Conferences |
| title | On subgroups product graph of finite groups |
| title_full | On subgroups product graph of finite groups |
| title_fullStr | On subgroups product graph of finite groups |
| title_full_unstemmed | On subgroups product graph of finite groups |
| title_short | On subgroups product graph of finite groups |
| title_sort | on subgroups product graph of finite groups |
| url | https://www.bio-conferences.org/articles/bioconf/pdf/2024/16/bioconf_iscku2024_00155.pdf |
| work_keys_str_mv | AT abdshakirjawad onsubgroupsproductgraphoffinitegroups AT shelashhayderb onsubgroupsproductgraphoffinitegroups |