Theory and Application of Interval-Valued Neutrosophic Line Graphs
Neutrosophic graphs are used to model inconsistent information and imprecise data about any real-life problem. It is regarded as a generalization of intuitionistic fuzzy graphs. Since interval-valued neutrosophic sets are more accurate, compatible, and flexible than single neutrosophic sets, interva...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/5692756 |
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| _version_ | 1832559636488650752 |
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| author | Keneni Abera Tola V. N. Srinivasa Rao Repalle Mamo Abebe Ashebo |
| author_facet | Keneni Abera Tola V. N. Srinivasa Rao Repalle Mamo Abebe Ashebo |
| author_sort | Keneni Abera Tola |
| collection | DOAJ |
| description | Neutrosophic graphs are used to model inconsistent information and imprecise data about any real-life problem. It is regarded as a generalization of intuitionistic fuzzy graphs. Since interval-valued neutrosophic sets are more accurate, compatible, and flexible than single neutrosophic sets, interval-valued neutrosophic graphs (IVNGs) were defined. The interval-valued neutrosophic graph is a fundamental issue in graph theory that has wide applications in the real world. Also, problems may arise when partial ignorance exists in the datasets of membership [0, 1], and then, the concept of IVNG is crucial to represent the problems. Line graphs of neutrosophic graphs are significant due to their ability to represent and analyze uncertain or indeterminate information about edge relationships and complex networks in graphs. However, there is a research gap on the line graph of interval-valued neutrosophic graphs. In this paper, we introduce the theory of an interval-valued neutrosophic line graph (IVNLG) and its application. In line with that, some mathematical properties such as weak vertex isomorphism, weak edge isomorphism, effective edge, and other properties of IVNLGs are proposed. In addition, we defined the vertex degree of IVNLG with some properties, and by presenting several theorems and propositions, the relationship between fuzzy graph extensions and IVNLGs was explored. Finally, an overview of the algorithm used to solve the problems and the practical application of the introduced graphs were provided. |
| format | Article |
| id | doaj-art-8db4530822604263950c4c5ce1da6caa |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-8db4530822604263950c4c5ce1da6caa2025-02-03T01:29:36ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/5692756Theory and Application of Interval-Valued Neutrosophic Line GraphsKeneni Abera Tola0V. N. Srinivasa Rao Repalle1Mamo Abebe Ashebo2Department of MathematicsDepartment of MathematicsDepartment of MathematicsNeutrosophic graphs are used to model inconsistent information and imprecise data about any real-life problem. It is regarded as a generalization of intuitionistic fuzzy graphs. Since interval-valued neutrosophic sets are more accurate, compatible, and flexible than single neutrosophic sets, interval-valued neutrosophic graphs (IVNGs) were defined. The interval-valued neutrosophic graph is a fundamental issue in graph theory that has wide applications in the real world. Also, problems may arise when partial ignorance exists in the datasets of membership [0, 1], and then, the concept of IVNG is crucial to represent the problems. Line graphs of neutrosophic graphs are significant due to their ability to represent and analyze uncertain or indeterminate information about edge relationships and complex networks in graphs. However, there is a research gap on the line graph of interval-valued neutrosophic graphs. In this paper, we introduce the theory of an interval-valued neutrosophic line graph (IVNLG) and its application. In line with that, some mathematical properties such as weak vertex isomorphism, weak edge isomorphism, effective edge, and other properties of IVNLGs are proposed. In addition, we defined the vertex degree of IVNLG with some properties, and by presenting several theorems and propositions, the relationship between fuzzy graph extensions and IVNLGs was explored. Finally, an overview of the algorithm used to solve the problems and the practical application of the introduced graphs were provided.http://dx.doi.org/10.1155/2024/5692756 |
| spellingShingle | Keneni Abera Tola V. N. Srinivasa Rao Repalle Mamo Abebe Ashebo Theory and Application of Interval-Valued Neutrosophic Line Graphs Journal of Mathematics |
| title | Theory and Application of Interval-Valued Neutrosophic Line Graphs |
| title_full | Theory and Application of Interval-Valued Neutrosophic Line Graphs |
| title_fullStr | Theory and Application of Interval-Valued Neutrosophic Line Graphs |
| title_full_unstemmed | Theory and Application of Interval-Valued Neutrosophic Line Graphs |
| title_short | Theory and Application of Interval-Valued Neutrosophic Line Graphs |
| title_sort | theory and application of interval valued neutrosophic line graphs |
| url | http://dx.doi.org/10.1155/2024/5692756 |
| work_keys_str_mv | AT keneniaberatola theoryandapplicationofintervalvaluedneutrosophiclinegraphs AT vnsrinivasaraorepalle theoryandapplicationofintervalvaluedneutrosophiclinegraphs AT mamoabebeashebo theoryandapplicationofintervalvaluedneutrosophiclinegraphs |