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Published in:   Vol. 3 Issue 3 Date of Publication:   December 2014

Few More Results on Sum Labeling of Split Graphs

J.Gerard Rozario

Page(s):   252-254 ISSN:   2278-2397
DOI:   10.20894/IJCOA.101.003.003.022 Publisher:   Integrated Intelligent Research (IIR)

A sum labeling is a mapping from the vertices of G into the positive integers such that, for any two vertices u, v V (G) with labels (u) and (v), respectively, (uv) is an edge iff (u) + (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.