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International Journal of Computing Algorithm, Vol 3(3), June 2014
ISSN(Print):2278-2397
Website: www.ijcoa.com
Few More Results on Sum Labeling of Split Graphs
J. Gerard Rozario
Department of Mathematics, IFET College of Engineering, Villupuram, Tamil Nadu, India
E-mail: rozario.gerard@yahoo.com
Abstract
A sum labeling is a mapping λ from the vertices of G into the positive integers such that, for
any two vertices u, v ϵ V (G) with labels λ(u) and λ(v), respectively, (uv) is an edge iff λ(u) +
λ(v) is the label of another vertex in V (G). Any graph supporting such a labeling is called a
sum graph. It is necessary to add (as a disjoint union) a component to sum label a graph. This
disconnected component is a set of isolated vertices known as isolates and the labeling
scheme that requires the fewest isolates is termed optimal. The number of isolates required
for a graph to support a sum labeling is known as the sum number of the graph. In this paper,
we will obtain optimal sum labeling scheme for path union of split graph of star,
K , ⨀Spl(P ) and K , ⨀Spl(K , ).

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