Subdivided Shell Flower Graphs are Odd Graceful

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Year:
2014
Type of Publication:
Article
Keywords:
Odd Graceful Labeling, Shell Graph, Subdivided Shell Graph, Subdivided Shell Flower Graph
Authors:
J. Jeba Jesintha; K. Ezhilarasi Hilda
Journal:
IJISM
Volume:
2
Number:
4
Pages:
402-404
Month:
July
Abstract:
A graph G with ‘q’ edges is said to be odd graceful if there is an injection ‘f’ from V(G) to {0, 1, 2, . . . ,(2q- 1)} such that when each edge xy is assigned the label│f(x) – f(y)│, the resulting edge labels are {1, 3, 5, . . . ,(2q-1)}. Shell graphs, also known as fans are the join of K1 and Pm , the path with ‘m’ vertices. When each edge in the path alone are sub divided, we say that it is a sub divided shell graph. A multiple subdivided shell is defined to be a collection of edge disjoint sub divided shells that have their apex in common. We define a Subdivided shell flower graph is one vertex union of three subdivided shells. We call each subdivided shell in this graph as a petal. In this paper we prove that all subdivided shell flower graphs are odd graceful.

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