Face irregular evaluations of family of grids
Let [Formula: see text] be a connected plane graph. Let [Formula: see text] be a k-labeling where [Formula: see text] and [Formula: see text]. The weight of a face f under ρ is defined as [Formula: see text]. Then ρ is called a face irregular labeling of type [Formula: see text] if [Formula: see tex...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2025-01-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2024.2368126 |
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| _version_ | 1849763364001021952 |
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| author | Jalal Hatem Hussein Bayati Ali Ovais Abid Mahboob Muhammad Waheed Rasheed |
| author_facet | Jalal Hatem Hussein Bayati Ali Ovais Abid Mahboob Muhammad Waheed Rasheed |
| author_sort | Jalal Hatem Hussein Bayati |
| collection | DOAJ |
| description | Let [Formula: see text] be a connected plane graph. Let [Formula: see text] be a k-labeling where [Formula: see text] and [Formula: see text]. The weight of a face f under ρ is defined as [Formula: see text]. Then ρ is called a face irregular labeling of type [Formula: see text] if [Formula: see text] for any two faces [Formula: see text]. The face irregular strength of G is the smallest integer k such that G admits a face irreg ular k-labeling. In this paper we determine the face irregular strength of the grid graph [Formula: see text] under a labeling of type [Formula: see text]. |
| format | Article |
| id | doaj-art-ad694bf93a704ea38ef9f3eeba9cba43 |
| institution | DOAJ |
| issn | 0972-8600 2543-3474 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj-art-ad694bf93a704ea38ef9f3eeba9cba432025-08-20T03:05:26ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742025-01-0122111710.1080/09728600.2024.2368126Face irregular evaluations of family of gridsJalal Hatem Hussein Bayati0Ali Ovais1Abid Mahboob2Muhammad Waheed Rasheed3Department of Mathematics, College and Science for Woman, University of Baghdad, Baghdad, IraqUniversity of Engineering and Technology, Lahore, PakistanDepartment of Mathematics, Division of Science and Technology, University of Education, Lahore, PakistanDepartment of Mathematics, Division of Science and Technology, University of Education, Lahore, PakistanLet [Formula: see text] be a connected plane graph. Let [Formula: see text] be a k-labeling where [Formula: see text] and [Formula: see text]. The weight of a face f under ρ is defined as [Formula: see text]. Then ρ is called a face irregular labeling of type [Formula: see text] if [Formula: see text] for any two faces [Formula: see text]. The face irregular strength of G is the smallest integer k such that G admits a face irreg ular k-labeling. In this paper we determine the face irregular strength of the grid graph [Formula: see text] under a labeling of type [Formula: see text].https://www.tandfonline.com/doi/10.1080/09728600.2024.2368126Face irregular labeling of typeface irregular strengthCartesian Product of path graphs |
| spellingShingle | Jalal Hatem Hussein Bayati Ali Ovais Abid Mahboob Muhammad Waheed Rasheed Face irregular evaluations of family of grids AKCE International Journal of Graphs and Combinatorics Face irregular labeling of type face irregular strength Cartesian Product of path graphs |
| title | Face irregular evaluations of family of grids |
| title_full | Face irregular evaluations of family of grids |
| title_fullStr | Face irregular evaluations of family of grids |
| title_full_unstemmed | Face irregular evaluations of family of grids |
| title_short | Face irregular evaluations of family of grids |
| title_sort | face irregular evaluations of family of grids |
| topic | Face irregular labeling of type face irregular strength Cartesian Product of path graphs |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2024.2368126 |
| work_keys_str_mv | AT jalalhatemhusseinbayati faceirregularevaluationsoffamilyofgrids AT aliovais faceirregularevaluationsoffamilyofgrids AT abidmahboob faceirregularevaluationsoffamilyofgrids AT muhammadwaheedrasheed faceirregularevaluationsoffamilyofgrids |