A study on the varieties of equivalent cordial labeling graphs
The concepts of cordial labeling, signed product cordiality, and logical cordiality have been introduced independently by different researchers as distinct labeling schemes. In this paper, we demonstrate the equivalence of these concepts. Specifically, we prove that a graph $ G $ is cordial if and o...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241653 |
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| author | M. E. Abdel-Aal S. A. Bashammakh |
| author_facet | M. E. Abdel-Aal S. A. Bashammakh |
| author_sort | M. E. Abdel-Aal |
| collection | DOAJ |
| description | The concepts of cordial labeling, signed product cordiality, and logical cordiality have been introduced independently by different researchers as distinct labeling schemes. In this paper, we demonstrate the equivalence of these concepts. Specifically, we prove that a graph $ G $ is cordial if and only if it is signed product cordial, if and only if it is logically cordial. Additionally, we establish that a graph $ G $ admits permuted cordial labeling if and only if it exhibits cubic roots cordial labeling. Furthermore, we leverage this newfound equivalence to analyze the cordiality properties of several standard graphs. |
| format | Article |
| id | doaj-art-9126df5cb5924532ac4b09b34ec3d433 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-9126df5cb5924532ac4b09b34ec3d4332025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912347203473310.3934/math.20241653A study on the varieties of equivalent cordial labeling graphsM. E. Abdel-Aal0S. A. Bashammakh1Department of Mathematics, Faculty of Science, Banha University, Banha 13518, EgyptMathematics and Statistics Department, Faculty of Science, University of Jeddah, P. O. Box 80327, Jeddah 21589, Saudi ArabiaThe concepts of cordial labeling, signed product cordiality, and logical cordiality have been introduced independently by different researchers as distinct labeling schemes. In this paper, we demonstrate the equivalence of these concepts. Specifically, we prove that a graph $ G $ is cordial if and only if it is signed product cordial, if and only if it is logically cordial. Additionally, we establish that a graph $ G $ admits permuted cordial labeling if and only if it exhibits cubic roots cordial labeling. Furthermore, we leverage this newfound equivalence to analyze the cordiality properties of several standard graphs.https://www.aimspress.com/article/doi/10.3934/math.20241653graph labelingcordial graphsigned product cordiallogical cordial graph |
| spellingShingle | M. E. Abdel-Aal S. A. Bashammakh A study on the varieties of equivalent cordial labeling graphs AIMS Mathematics graph labeling cordial graph signed product cordial logical cordial graph |
| title | A study on the varieties of equivalent cordial labeling graphs |
| title_full | A study on the varieties of equivalent cordial labeling graphs |
| title_fullStr | A study on the varieties of equivalent cordial labeling graphs |
| title_full_unstemmed | A study on the varieties of equivalent cordial labeling graphs |
| title_short | A study on the varieties of equivalent cordial labeling graphs |
| title_sort | study on the varieties of equivalent cordial labeling graphs |
| topic | graph labeling cordial graph signed product cordial logical cordial graph |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241653 |
| work_keys_str_mv | AT meabdelaal astudyonthevarietiesofequivalentcordiallabelinggraphs AT sabashammakh astudyonthevarietiesofequivalentcordiallabelinggraphs AT meabdelaal studyonthevarietiesofequivalentcordiallabelinggraphs AT sabashammakh studyonthevarietiesofequivalentcordiallabelinggraphs |