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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