General, General Weak, Anti, Balanced, and Semi-Neutrosophic Graph
Graph classes categorize graphs based on shared properties or structures, and numerous such classes have been proposed over time. In 1965, Zadeh [43] introduced a framework for managing uncertainty, which later inspired Rosenfeld [28, 31] to develop fuzzy graph theory in 1975. A Neutrosophic Graph,...
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| Format: | Article |
| Language: | English |
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University of New Mexico
2025-06-01
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| Series: | Neutrosophic Sets and Systems |
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| Online Access: | https://fs.unm.edu/NSS/23AntiBalanced.pdf |
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| _version_ | 1849232897344536576 |
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| author | Takaaki Fujita Florentin Smarandache |
| author_facet | Takaaki Fujita Florentin Smarandache |
| author_sort | Takaaki Fujita |
| collection | DOAJ |
| description | Graph classes categorize graphs based on shared properties or structures, and numerous such classes have been proposed over time. In 1965, Zadeh [43] introduced a framework for managing uncertainty, which later inspired Rosenfeld [28, 31] to develop fuzzy graph theory in 1975. A Neutrosophic Graph, as a generalization of a Fuzzy Graph, associates each vertex and edge with three membership values representing truth, indeterminacy, and falsity. This allows Neutrosophic Graphs to handle uncertain, vague, or contradictory information more effectively. This paper aims to expand the study of Neutrosophic Graphs by proposing new graph classes, specifically the General-Neutrosophic Graph, Anti-Neutrosophic Graph, *-Balanced-Neutrosophic Graph, and Semi-Neutrosophic Graph. |
| format | Article |
| id | doaj-art-4d1e40006ed84a5688220529f688b8ed |
| institution | Kabale University |
| issn | 2331-6055 2331-608X |
| language | English |
| publishDate | 2025-06-01 |
| publisher | University of New Mexico |
| record_format | Article |
| series | Neutrosophic Sets and Systems |
| spelling | doaj-art-4d1e40006ed84a5688220529f688b8ed2025-08-20T16:37:15ZengUniversity of New MexicoNeutrosophic Sets and Systems2331-60552331-608X2025-06-018539843510.5281/zenodo.15294849General, General Weak, Anti, Balanced, and Semi-Neutrosophic GraphTakaaki Fujita Florentin SmarandacheGraph classes categorize graphs based on shared properties or structures, and numerous such classes have been proposed over time. In 1965, Zadeh [43] introduced a framework for managing uncertainty, which later inspired Rosenfeld [28, 31] to develop fuzzy graph theory in 1975. A Neutrosophic Graph, as a generalization of a Fuzzy Graph, associates each vertex and edge with three membership values representing truth, indeterminacy, and falsity. This allows Neutrosophic Graphs to handle uncertain, vague, or contradictory information more effectively. This paper aims to expand the study of Neutrosophic Graphs by proposing new graph classes, specifically the General-Neutrosophic Graph, Anti-Neutrosophic Graph, *-Balanced-Neutrosophic Graph, and Semi-Neutrosophic Graph.https://fs.unm.edu/NSS/23AntiBalanced.pdfneutrosophic graphbalanced-neutrosophic graphgeneral-neutrosophic graphantineutrosophic graphsemi-neutrosophic graph |
| spellingShingle | Takaaki Fujita Florentin Smarandache General, General Weak, Anti, Balanced, and Semi-Neutrosophic Graph Neutrosophic Sets and Systems neutrosophic graph balanced-neutrosophic graph general-neutrosophic graph antineutrosophic graph semi-neutrosophic graph |
| title | General, General Weak, Anti, Balanced, and Semi-Neutrosophic Graph |
| title_full | General, General Weak, Anti, Balanced, and Semi-Neutrosophic Graph |
| title_fullStr | General, General Weak, Anti, Balanced, and Semi-Neutrosophic Graph |
| title_full_unstemmed | General, General Weak, Anti, Balanced, and Semi-Neutrosophic Graph |
| title_short | General, General Weak, Anti, Balanced, and Semi-Neutrosophic Graph |
| title_sort | general general weak anti balanced and semi neutrosophic graph |
| topic | neutrosophic graph balanced-neutrosophic graph general-neutrosophic graph antineutrosophic graph semi-neutrosophic graph |
| url | https://fs.unm.edu/NSS/23AntiBalanced.pdf |
| work_keys_str_mv | AT takaakifujita generalgeneralweakantibalancedandsemineutrosophicgraph AT florentinsmarandache generalgeneralweakantibalancedandsemineutrosophicgraph |