Fermatean Neutrosophic Fuzzy Graphs: A Study on the Winner Index with Enhancing Election Analysis
In this article, we discuss the fermatean neutrosophic graph of Wiener index, which is an essential topological index formed according to geodesical distance of vertices. The Wiener index is an important factor to describe the structure of a graph and we defined it in relation to fermatean neutrosop...
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| Format: | Article |
| Language: | English |
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University of New Mexico
2025-04-01
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| Series: | Neutrosophic Sets and Systems |
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| Online Access: | https://fs.unm.edu/NSS/8FermateanNeutrosophic.pdf |
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| author | Wadei Fares AL-omeri Kaviyarasu M M. Rajeshwari |
| author_facet | Wadei Fares AL-omeri Kaviyarasu M M. Rajeshwari |
| author_sort | Wadei Fares AL-omeri |
| collection | DOAJ |
| description | In this article, we discuss the fermatean neutrosophic graph of Wiener index, which is an essential topological index formed according to geodesical distance of vertices. The Wiener index is an important factor to describe the structure of a graph and we defined it in relation to fermatean neutrosophic graphs and computed it for some specific fermatean neutrosophic graph structures including complete fermatean neutrosophic graphs, cycles and trees. Subsequently, the Wiener index is compared with the connectivity index, a core-degree based parameter, using a sequence of theorems. As an application the study responds to the difficulties in election analysis in democratic environments where voter choices are often nuanced an unpredictable and the methods of measurement are not sensitive enough to capture these changes. To improve the modeling of election data, this work employs fermatean neutrosophic graphs (FNGs) and the Wiener index, which distinguish nodes that represent leadership qualities, policy suggestions, and public commitment as well as the relationship between these nodes. This approach manages uncertainty and indeterminacy well and provides a sound method of enhancing the measurability and credibility of analytical techniques in managing complicated events like elections. |
| format | Article |
| id | doaj-art-3ee56cf2ad0e42e9807dcbe1d9d70e2c |
| institution | Kabale University |
| issn | 2331-6055 2331-608X |
| language | English |
| publishDate | 2025-04-01 |
| publisher | University of New Mexico |
| record_format | Article |
| series | Neutrosophic Sets and Systems |
| spelling | doaj-art-3ee56cf2ad0e42e9807dcbe1d9d70e2c2025-08-25T10:12:09ZengUniversity of New MexicoNeutrosophic Sets and Systems2331-60552331-608X2025-04-018012814810.5281/zenodo.14707336Fermatean Neutrosophic Fuzzy Graphs: A Study on the Winner Index with Enhancing Election AnalysisWadei Fares AL-omeriKaviyarasu MM. RajeshwariIn this article, we discuss the fermatean neutrosophic graph of Wiener index, which is an essential topological index formed according to geodesical distance of vertices. The Wiener index is an important factor to describe the structure of a graph and we defined it in relation to fermatean neutrosophic graphs and computed it for some specific fermatean neutrosophic graph structures including complete fermatean neutrosophic graphs, cycles and trees. Subsequently, the Wiener index is compared with the connectivity index, a core-degree based parameter, using a sequence of theorems. As an application the study responds to the difficulties in election analysis in democratic environments where voter choices are often nuanced an unpredictable and the methods of measurement are not sensitive enough to capture these changes. To improve the modeling of election data, this work employs fermatean neutrosophic graphs (FNGs) and the Wiener index, which distinguish nodes that represent leadership qualities, policy suggestions, and public commitment as well as the relationship between these nodes. This approach manages uncertainty and indeterminacy well and provides a sound method of enhancing the measurability and credibility of analytical techniques in managing complicated events like elections. https://fs.unm.edu/NSS/8FermateanNeutrosophic.pdffuzzy graphfn gwinner indexuncertainty modelingdecision making |
| spellingShingle | Wadei Fares AL-omeri Kaviyarasu M M. Rajeshwari Fermatean Neutrosophic Fuzzy Graphs: A Study on the Winner Index with Enhancing Election Analysis Neutrosophic Sets and Systems fuzzy graph fn g winner index uncertainty modeling decision making |
| title | Fermatean Neutrosophic Fuzzy Graphs: A Study on the Winner Index with Enhancing Election Analysis |
| title_full | Fermatean Neutrosophic Fuzzy Graphs: A Study on the Winner Index with Enhancing Election Analysis |
| title_fullStr | Fermatean Neutrosophic Fuzzy Graphs: A Study on the Winner Index with Enhancing Election Analysis |
| title_full_unstemmed | Fermatean Neutrosophic Fuzzy Graphs: A Study on the Winner Index with Enhancing Election Analysis |
| title_short | Fermatean Neutrosophic Fuzzy Graphs: A Study on the Winner Index with Enhancing Election Analysis |
| title_sort | fermatean neutrosophic fuzzy graphs a study on the winner index with enhancing election analysis |
| topic | fuzzy graph fn g winner index uncertainty modeling decision making |
| url | https://fs.unm.edu/NSS/8FermateanNeutrosophic.pdf |
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