On \(k\)-graceful labeling of pendant edge extension of complete bipartite graphs
For any two positive integers \(m,n\), we denote the graph \(K_{m,n}\odot K_1\) by \(G\). Ma Ke-Jie proposed a conjecture [9] that pendant edge extension of a complete bipartite graph is a \(k\)-graceful graph for \(k \ge 2\). In this paper we prove his conjecture for \(n\le m < n^2+\lfloor\f...
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| Date: | 2018 |
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| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/224 |
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| Journal Title: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-2242018-07-24T22:56:15Z On \(k\)-graceful labeling of pendant edge extension of complete bipartite graphs Bhoumik, Soumya Mitra, Sarbari \(k\)-graceful labeling, complete bipartite graph, corona, \(1\)-crown 05C78 For any two positive integers \(m,n\), we denote the graph \(K_{m,n}\odot K_1\) by \(G\). Ma Ke-Jie proposed a conjecture [9] that pendant edge extension of a complete bipartite graph is a \(k\)-graceful graph for \(k \ge 2\). In this paper we prove his conjecture for \(n\le m < n^2+\lfloor\frac{k}{n}\rfloor+ r\). Lugansk National Taras Shevchenko University 2018-07-25 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/224 Algebra and Discrete Mathematics; Vol 25, No 2 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/224/pdf Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-07-24T22:56:15Z |
| collection |
OJS |
| language |
English |
| topic |
\(k\)-graceful labeling complete bipartite graph corona \(1\)-crown 05C78 |
| spellingShingle |
\(k\)-graceful labeling complete bipartite graph corona \(1\)-crown 05C78 Bhoumik, Soumya Mitra, Sarbari On \(k\)-graceful labeling of pendant edge extension of complete bipartite graphs |
| topic_facet |
\(k\)-graceful labeling complete bipartite graph corona \(1\)-crown 05C78 |
| format |
Article |
| author |
Bhoumik, Soumya Mitra, Sarbari |
| author_facet |
Bhoumik, Soumya Mitra, Sarbari |
| author_sort |
Bhoumik, Soumya |
| title |
On \(k\)-graceful labeling of pendant edge extension of complete bipartite graphs |
| title_short |
On \(k\)-graceful labeling of pendant edge extension of complete bipartite graphs |
| title_full |
On \(k\)-graceful labeling of pendant edge extension of complete bipartite graphs |
| title_fullStr |
On \(k\)-graceful labeling of pendant edge extension of complete bipartite graphs |
| title_full_unstemmed |
On \(k\)-graceful labeling of pendant edge extension of complete bipartite graphs |
| title_sort |
on \(k\)-graceful labeling of pendant edge extension of complete bipartite graphs |
| description |
For any two positive integers \(m,n\), we denote the graph \(K_{m,n}\odot K_1\) by \(G\). Ma Ke-Jie proposed a conjecture [9] that pendant edge extension of a complete bipartite graph is a \(k\)-graceful graph for \(k \ge 2\). In this paper we prove his conjecture for \(n\le m < n^2+\lfloor\frac{k}{n}\rfloor+ r\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/224 |
| work_keys_str_mv |
AT bhoumiksoumya onkgracefullabelingofpendantedgeextensionofcompletebipartitegraphs AT mitrasarbari onkgracefullabelingofpendantedgeextensionofcompletebipartitegraphs |
| first_indexed |
2025-07-17T10:35:22Z |
| last_indexed |
2025-07-17T10:35:22Z |
| _version_ |
1837890035084427264 |