ALPHA LABELINGS OF DISJOINT UNION OF HAIRY CYCLES

G. Rajasekaran     (Department of Mathematics, Vellore Institute of Technology, Vellore – 632014, Tamil Nadu, India)
L. Uma     (Department of Mathematics, Vellore Institute of Technology, Vellore – 632014, Tamil Nadu, India)

Abstract


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).


Keywords


Hairy Cycles, Graceful Valuation, Alpha Valuation

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References


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DOI: http://dx.doi.org/10.15826/umj.2024.1.011

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