Prime labelings on planar grid graphs
It is known that for any prime p and any integer n such that 1≤n≤p there exists a prime labeling on the pxn planar grid graph PpxPn. We show that PpxPn has a prime labeling for any odd prime p and any integer n such that that p<n≤p2.
| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Georgia Southern University
2022-03-01
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| Series: | Theory and Applications of Graphs |
| Subjects: | |
| Online Access: | https://digitalcommons.georgiasouthern.edu/tag/vol9/iss1/6/ |
| _version_ | 1819062367253692416 |
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| author | Stephen James Curran |
| author_facet | Stephen James Curran |
| author_sort | Stephen James Curran |
| collection | DOAJ |
| description | It is known that for any prime p and any integer n such that 1≤n≤p there exists a prime labeling on the pxn planar grid graph PpxPn. We show that PpxPn has a prime labeling for any odd prime p and any integer n such that that p<n≤p2. |
| first_indexed | 2024-12-21T14:57:39Z |
| format | Article |
| id | doaj.art-10578f24d5c04c478dd8ff2110669f75 |
| institution | Directory Open Access Journal |
| issn | 2470-9859 |
| language | English |
| last_indexed | 2024-12-21T14:57:39Z |
| publishDate | 2022-03-01 |
| publisher | Georgia Southern University |
| record_format | Article |
| series | Theory and Applications of Graphs |
| spelling | doaj.art-10578f24d5c04c478dd8ff2110669f752022-12-21T18:59:41ZengGeorgia Southern UniversityTheory and Applications of Graphs2470-98592022-03-019111410.20429/tag.2022.090106Prime labelings on planar grid graphsStephen James Curran0University of Pittsburgh - JohnstownIt is known that for any prime p and any integer n such that 1≤n≤p there exists a prime labeling on the pxn planar grid graph PpxPn. We show that PpxPn has a prime labeling for any odd prime p and any integer n such that that p<n≤p2.https://digitalcommons.georgiasouthern.edu/tag/vol9/iss1/6/prime graphprime labelingplanar grid graphcartesian product of paths |
| spellingShingle | Stephen James Curran Prime labelings on planar grid graphs Theory and Applications of Graphs prime graph prime labeling planar grid graph cartesian product of paths |
| title | Prime labelings on planar grid graphs |
| title_full | Prime labelings on planar grid graphs |
| title_fullStr | Prime labelings on planar grid graphs |
| title_full_unstemmed | Prime labelings on planar grid graphs |
| title_short | Prime labelings on planar grid graphs |
| title_sort | prime labelings on planar grid graphs |
| topic | prime graph prime labeling planar grid graph cartesian product of paths |
| url | https://digitalcommons.georgiasouthern.edu/tag/vol9/iss1/6/ |
| work_keys_str_mv | AT stephenjamescurran primelabelingsonplanargridgraphs |