A Novel Approach for Cyclic Decompositions of Balanced Complete Bipartite Graphs into Infinite Graph Classes
Graph theory is considered an attractive field for finding the proof techniques in discrete mathematics. The results of graph theory have applications in many areas of social, computing, and natural sciences. Graph labelings and decompositions have received much attention in the literature. Several...
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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/10.1155/2022/9308708 |
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| author | A. El-Mesady Omar Bazighifan S. S. Askar |
| author_facet | A. El-Mesady Omar Bazighifan S. S. Askar |
| author_sort | A. El-Mesady |
| collection | DOAJ |
| description | Graph theory is considered an attractive field for finding the proof techniques in discrete mathematics. The results of graph theory have applications in many areas of social, computing, and natural sciences. Graph labelings and decompositions have received much attention in the literature. Several types of graph labeling were proposed for solving the problem of decomposing different graph classes. In the present paper, we propose a technique for labeling the vertices of a bipartite graph G with n edges, called orthogonal labeling, to yield cyclic decompositions of balanced complete bipartite graphs Kn,n by the graph G. By applying the proposed orthogonal labeling technique, we had constructed decompositions of Kn,n by paths, trees, one factorization, disjoint union of cycles, complete bipartite graphs, disjoint union of trees, caterpillars, and so forth. From the constructed results, we can confirm that the proposed orthogonal labeling technique is effective. |
| format | Article |
| id | doaj-art-c402ba8e04224ed18619817465ef2e0d |
| 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-c402ba8e04224ed18619817465ef2e0d2025-02-03T01:22:27ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/9308708A Novel Approach for Cyclic Decompositions of Balanced Complete Bipartite Graphs into Infinite Graph ClassesA. El-Mesady0Omar Bazighifan1S. S. Askar2Department of Physics and Engineering MathematicsSection of MathematicsDepartment of Statistics and Operations ResearchGraph theory is considered an attractive field for finding the proof techniques in discrete mathematics. The results of graph theory have applications in many areas of social, computing, and natural sciences. Graph labelings and decompositions have received much attention in the literature. Several types of graph labeling were proposed for solving the problem of decomposing different graph classes. In the present paper, we propose a technique for labeling the vertices of a bipartite graph G with n edges, called orthogonal labeling, to yield cyclic decompositions of balanced complete bipartite graphs Kn,n by the graph G. By applying the proposed orthogonal labeling technique, we had constructed decompositions of Kn,n by paths, trees, one factorization, disjoint union of cycles, complete bipartite graphs, disjoint union of trees, caterpillars, and so forth. From the constructed results, we can confirm that the proposed orthogonal labeling technique is effective.http://dx.doi.org/10.1155/2022/9308708 |
| spellingShingle | A. El-Mesady Omar Bazighifan S. S. Askar A Novel Approach for Cyclic Decompositions of Balanced Complete Bipartite Graphs into Infinite Graph Classes Journal of Function Spaces |
| title | A Novel Approach for Cyclic Decompositions of Balanced Complete Bipartite Graphs into Infinite Graph Classes |
| title_full | A Novel Approach for Cyclic Decompositions of Balanced Complete Bipartite Graphs into Infinite Graph Classes |
| title_fullStr | A Novel Approach for Cyclic Decompositions of Balanced Complete Bipartite Graphs into Infinite Graph Classes |
| title_full_unstemmed | A Novel Approach for Cyclic Decompositions of Balanced Complete Bipartite Graphs into Infinite Graph Classes |
| title_short | A Novel Approach for Cyclic Decompositions of Balanced Complete Bipartite Graphs into Infinite Graph Classes |
| title_sort | novel approach for cyclic decompositions of balanced complete bipartite graphs into infinite graph classes |
| url | http://dx.doi.org/10.1155/2022/9308708 |
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