On graphs with equal coprime index and clique number
AbstractRecently, Katre et al. introduced the concept of the coprime index of a graph. They asked to characterize the graphs for which the coprime index is the same as the clique number. In this paper, we partially solve this problem. In fact, we prove that the clique number and the coprime index of...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2023-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2023.2218442 |
| _version_ | 1797385671347798016 |
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| author | Chetan Patil Nilesh Khandekar Vinayak Joshi |
| author_facet | Chetan Patil Nilesh Khandekar Vinayak Joshi |
| author_sort | Chetan Patil |
| collection | DOAJ |
| description | AbstractRecently, Katre et al. introduced the concept of the coprime index of a graph. They asked to characterize the graphs for which the coprime index is the same as the clique number. In this paper, we partially solve this problem. In fact, we prove that the clique number and the coprime index of a zero-divisor graph of an ordered set and the zero-divisor graph of a ring [Formula: see text] coincide. Also, it is proved that the annihilating ideal graphs, the co-annihilating ideal graphs and the comaximal ideal graphs of commutative rings can be realized as the zero-divisor graphs of specially constructed posets. Hence the coprime index and the clique number coincide for these graphs as well. |
| first_indexed | 2024-03-08T21:57:39Z |
| format | Article |
| id | doaj.art-ff70fdc3b1ac4cb589f8f6e03bf37509 |
| institution | Directory Open Access Journal |
| issn | 0972-8600 2543-3474 |
| language | English |
| last_indexed | 2024-03-08T21:57:39Z |
| publishDate | 2023-09-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-ff70fdc3b1ac4cb589f8f6e03bf375092023-12-19T17:41:03ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742023-09-0120323524310.1080/09728600.2023.2218442On graphs with equal coprime index and clique numberChetan Patil0Nilesh Khandekar1Vinayak Joshi2Department of Mathematics, Savitribai Phule Pune University, Pune, Maharashtra, IndiaDepartment of Mathematics, Savitribai Phule Pune University, Pune, Maharashtra, IndiaDepartment of Mathematics, Savitribai Phule Pune University, Pune, Maharashtra, IndiaAbstractRecently, Katre et al. introduced the concept of the coprime index of a graph. They asked to characterize the graphs for which the coprime index is the same as the clique number. In this paper, we partially solve this problem. In fact, we prove that the clique number and the coprime index of a zero-divisor graph of an ordered set and the zero-divisor graph of a ring [Formula: see text] coincide. Also, it is proved that the annihilating ideal graphs, the co-annihilating ideal graphs and the comaximal ideal graphs of commutative rings can be realized as the zero-divisor graphs of specially constructed posets. Hence the coprime index and the clique number coincide for these graphs as well.https://www.tandfonline.com/doi/10.1080/09728600.2023.2218442Coprime labelingcoprime indexedge clique coverintersection numberzero-divisor graphsannihilating ideal graphs |
| spellingShingle | Chetan Patil Nilesh Khandekar Vinayak Joshi On graphs with equal coprime index and clique number AKCE International Journal of Graphs and Combinatorics Coprime labeling coprime index edge clique cover intersection number zero-divisor graphs annihilating ideal graphs |
| title | On graphs with equal coprime index and clique number |
| title_full | On graphs with equal coprime index and clique number |
| title_fullStr | On graphs with equal coprime index and clique number |
| title_full_unstemmed | On graphs with equal coprime index and clique number |
| title_short | On graphs with equal coprime index and clique number |
| title_sort | on graphs with equal coprime index and clique number |
| topic | Coprime labeling coprime index edge clique cover intersection number zero-divisor graphs annihilating ideal graphs |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2023.2218442 |
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