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: G. Rajasekaran, L. Uma
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
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).
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institution Kabale University
issn 2414-3952
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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
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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