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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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 |
| Subjects: | |
| Online Access: | https://umjuran.ru/index.php/umj/article/view/506 |
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| Summary: | 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). |
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| ISSN: | 2414-3952 |