ALPHA LABELINGS OF DISJOINT UNION OF HAIRY CYCLES
In this paper, we prove the following results: 1) the disjoint union of \(n\geq 2\) isomorphic copies of the graph which is obtained by adding a pendent edge to each vertices of the cycle of order 4 admits \(\alpha\)-valuation; 2) the disjoint union of two isomorphic copies of the graph which is obt...
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2024-07-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/506 |
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| author | G. Rajasekaran L. Uma |
| author_facet | G. Rajasekaran L. Uma |
| author_sort | G. Rajasekaran |
| collection | DOAJ |
| description | In this paper, we prove the following results: 1) the disjoint union of \(n\geq 2\) isomorphic copies of the graph which is obtained by adding a pendent edge to each vertices of the cycle of order 4 admits \(\alpha\)-valuation; 2) the disjoint union of two isomorphic copies of the graph which is obtained by adding \(n\geq 1\) pendent edge to each vertices of the cycle of order 4 is admits \(\alpha\)-valuation; 3) the disjoint union of two isomorphic copies of the graph obtained by adding a pendent edge to each vertex of the cycle of order \(4m\) admits \(\alpha\)-valuation; 4) the disjoint union of two non-isomorphic copies of the graph obtained by adding a pendent edge to each vertices of the cycle of order \(4m\) and \(4m-2\) admits \(\alpha\)-valuation; 5) the disjoint union of two isomorphic copies of the graph which is obtained by adding a pendant edge to each vertex of the cycle of order \(4m-1(4m+2)\) is admitted graceful (\(\alpha\)-valuation). |
| format | Article |
| id | doaj-art-35cb581c775f4e1f908feb07a3db90dc |
| institution | Kabale University |
| issn | 2414-3952 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-35cb581c775f4e1f908feb07a3db90dc2025-08-20T03:28:32ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522024-07-0110110.15826/umj.2024.1.011210ALPHA LABELINGS OF DISJOINT UNION OF HAIRY CYCLESG. Rajasekaran0L. Uma1Department of Mathematics, Vellore Institute of Technology, Vellore – 632014, Tamil NaduDepartment of Mathematics, Vellore Institute of Technology, Vellore – 632014, Tamil NaduIn this paper, we prove the following results: 1) the disjoint union of \(n\geq 2\) isomorphic copies of the graph which is obtained by adding a pendent edge to each vertices of the cycle of order 4 admits \(\alpha\)-valuation; 2) the disjoint union of two isomorphic copies of the graph which is obtained by adding \(n\geq 1\) pendent edge to each vertices of the cycle of order 4 is admits \(\alpha\)-valuation; 3) the disjoint union of two isomorphic copies of the graph obtained by adding a pendent edge to each vertex of the cycle of order \(4m\) admits \(\alpha\)-valuation; 4) the disjoint union of two non-isomorphic copies of the graph obtained by adding a pendent edge to each vertices of the cycle of order \(4m\) and \(4m-2\) admits \(\alpha\)-valuation; 5) the disjoint union of two isomorphic copies of the graph which is obtained by adding a pendant edge to each vertex of the cycle of order \(4m-1(4m+2)\) is admitted graceful (\(\alpha\)-valuation).https://umjuran.ru/index.php/umj/article/view/506hairy cycles, graceful valuation, alpha valuation |
| spellingShingle | G. Rajasekaran L. Uma ALPHA LABELINGS OF DISJOINT UNION OF HAIRY CYCLES Ural Mathematical Journal hairy cycles, graceful valuation, alpha valuation |
| title | ALPHA LABELINGS OF DISJOINT UNION OF HAIRY CYCLES |
| title_full | ALPHA LABELINGS OF DISJOINT UNION OF HAIRY CYCLES |
| title_fullStr | ALPHA LABELINGS OF DISJOINT UNION OF HAIRY CYCLES |
| title_full_unstemmed | ALPHA LABELINGS OF DISJOINT UNION OF HAIRY CYCLES |
| title_short | ALPHA LABELINGS OF DISJOINT UNION OF HAIRY CYCLES |
| title_sort | alpha labelings of disjoint union of hairy cycles |
| topic | hairy cycles, graceful valuation, alpha valuation |
| url | https://umjuran.ru/index.php/umj/article/view/506 |
| work_keys_str_mv | AT grajasekaran alphalabelingsofdisjointunionofhairycycles AT luma alphalabelingsofdisjointunionofhairycycles |