Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares
The subject of mutually orthogonal Latin squares (MOLSs) has fascinated researchers for many years. Although there is a number of intriguing results in this area, many open problems remain to which the answers seem as elusive as ever. Mutually orthogonal graph squares (MOGSs) are considered a genera...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2021-05-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/09728600.2021.1966349 |
| _version_ | 1818650782665277440 |
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| author | A. El-Mesady Shaaban M. Shaaban |
| author_facet | A. El-Mesady Shaaban M. Shaaban |
| author_sort | A. El-Mesady |
| collection | DOAJ |
| description | The subject of mutually orthogonal Latin squares (MOLSs) has fascinated researchers for many years. Although there is a number of intriguing results in this area, many open problems remain to which the answers seem as elusive as ever. Mutually orthogonal graph squares (MOGSs) are considered a generalization to MOLS. MOLS are considered an area of combinatorial design theory which has many applications in optical communications, cryptography, storage system design, wireless communications, communication protocols, and algorithm design and analysis, to mention just a few areas. In this paper, we introduce a technique for constructing the mutually orthogonal disjoint union of graphs squares and the generalization of the Kronecker product of MOGS as a generalization to the MacNeish’s Kronecker product of MOLS. These are useful for constructing many new results concerned with the MOGS. |
| first_indexed | 2024-12-17T01:55:41Z |
| format | Article |
| id | doaj.art-5177d96b6f34435498d4a33110c52383 |
| institution | Directory Open Access Journal |
| issn | 0972-8600 2543-3474 |
| language | English |
| last_indexed | 2024-12-17T01:55:41Z |
| publishDate | 2021-05-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-5177d96b6f34435498d4a33110c523832022-12-21T22:07:58ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742021-05-0118211712210.1080/09728600.2021.19663491966349Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squaresA. El-Mesady0Shaaban M. Shaaban1Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia UniversityDepartment of Engineering Basic Science, Faculty of Engineering, Menoufia UniversityThe subject of mutually orthogonal Latin squares (MOLSs) has fascinated researchers for many years. Although there is a number of intriguing results in this area, many open problems remain to which the answers seem as elusive as ever. Mutually orthogonal graph squares (MOGSs) are considered a generalization to MOLS. MOLS are considered an area of combinatorial design theory which has many applications in optical communications, cryptography, storage system design, wireless communications, communication protocols, and algorithm design and analysis, to mention just a few areas. In this paper, we introduce a technique for constructing the mutually orthogonal disjoint union of graphs squares and the generalization of the Kronecker product of MOGS as a generalization to the MacNeish’s Kronecker product of MOLS. These are useful for constructing many new results concerned with the MOGS.http://dx.doi.org/10.1080/09728600.2021.1966349latin squaresgraph squareskronecker product |
| spellingShingle | A. El-Mesady Shaaban M. Shaaban Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares AKCE International Journal of Graphs and Combinatorics latin squares graph squares kronecker product |
| title | Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares |
| title_full | Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares |
| title_fullStr | Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares |
| title_full_unstemmed | Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares |
| title_short | Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares |
| title_sort | generalization of macneish s kronecker product theorem of mutually orthogonal latin squares |
| topic | latin squares graph squares kronecker product |
| url | http://dx.doi.org/10.1080/09728600.2021.1966349 |
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