Decompositions of Circulant-Balanced Complete Multipartite Graphs Based on a Novel Labelling Approach
For applied scientists and engineers, graph theory is a strong and vital tool for evaluating and inventing solutions for a variety of issues. Graph theory is extremely important in complex systems, particularly in computer science. Many scientific areas use graph theory, including biological science...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/2017936 |
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| author | A. El-Mesady Omar Bazighifan |
| author_facet | A. El-Mesady Omar Bazighifan |
| author_sort | A. El-Mesady |
| collection | DOAJ |
| description | For applied scientists and engineers, graph theory is a strong and vital tool for evaluating and inventing solutions for a variety of issues. Graph theory is extremely important in complex systems, particularly in computer science. Many scientific areas use graph theory, including biological sciences, engineering, coding, and operational research. A strategy for the orthogonal labelling of a bipartite graph G with n edges has been proposed in the literature, yielding cyclic decompositions of balanced complete bipartite graphs Kn,n by the graph G. A generalization to circulant-balanced complete multipartite graphs Kn,n,⋯,n⏟m;m,n≥2, is our objective here. In this paper, we expand the orthogonal labelling approach used to generate cyclic decompositions for Kn,n to a generalized orthogonal labelling approach that may be used for decomposing Kn,n,⋯,n⏟m. We can decompose Kn,n,⋯,n⏟m into distinct graph classes based on the proposed generalized orthogonal labelling approach. |
| format | Article |
| id | doaj-art-5dd45cf107f34cd3b2ea4e239f9298c9 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-5dd45cf107f34cd3b2ea4e239f9298c92025-02-03T01:20:06ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/2017936Decompositions of Circulant-Balanced Complete Multipartite Graphs Based on a Novel Labelling ApproachA. El-Mesady0Omar Bazighifan1Department of Physics and Engineering MathematicsDepartment of MathematicsFor applied scientists and engineers, graph theory is a strong and vital tool for evaluating and inventing solutions for a variety of issues. Graph theory is extremely important in complex systems, particularly in computer science. Many scientific areas use graph theory, including biological sciences, engineering, coding, and operational research. A strategy for the orthogonal labelling of a bipartite graph G with n edges has been proposed in the literature, yielding cyclic decompositions of balanced complete bipartite graphs Kn,n by the graph G. A generalization to circulant-balanced complete multipartite graphs Kn,n,⋯,n⏟m;m,n≥2, is our objective here. In this paper, we expand the orthogonal labelling approach used to generate cyclic decompositions for Kn,n to a generalized orthogonal labelling approach that may be used for decomposing Kn,n,⋯,n⏟m. We can decompose Kn,n,⋯,n⏟m into distinct graph classes based on the proposed generalized orthogonal labelling approach.http://dx.doi.org/10.1155/2022/2017936 |
| spellingShingle | A. El-Mesady Omar Bazighifan Decompositions of Circulant-Balanced Complete Multipartite Graphs Based on a Novel Labelling Approach Journal of Function Spaces |
| title | Decompositions of Circulant-Balanced Complete Multipartite Graphs Based on a Novel Labelling Approach |
| title_full | Decompositions of Circulant-Balanced Complete Multipartite Graphs Based on a Novel Labelling Approach |
| title_fullStr | Decompositions of Circulant-Balanced Complete Multipartite Graphs Based on a Novel Labelling Approach |
| title_full_unstemmed | Decompositions of Circulant-Balanced Complete Multipartite Graphs Based on a Novel Labelling Approach |
| title_short | Decompositions of Circulant-Balanced Complete Multipartite Graphs Based on a Novel Labelling Approach |
| title_sort | decompositions of circulant balanced complete multipartite graphs based on a novel labelling approach |
| url | http://dx.doi.org/10.1155/2022/2017936 |
| work_keys_str_mv | AT aelmesady decompositionsofcirculantbalancedcompletemultipartitegraphsbasedonanovellabellingapproach AT omarbazighifan decompositionsofcirculantbalancedcompletemultipartitegraphsbasedonanovellabellingapproach |