Further Results on Pair Sum Labeling of Trees
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Abstract
Let G be a (<i>p,q</i>) graph. An injective map <i>f</i>:<i>V</i>(<i>G</i>)→﹛±1,±2,...±<i>p</i>﹜is called a pair sum labeling if the induced edge function, <i>f<sub>e</sub></i>:<i>E</i>(<i>G</i>)→<i>Z</i>-﹛0﹜defined by <i>f<sub>e</sub></i>(uv)=<i>f</i>(<i>u</i>)+<i>f</i>(<i>v</i>) is one-one and <i>f<sub>e</sub></i>(<i>E</i>(<i>G</i>)) is either of the form {±<i>k</i><sub>1</sub>,±<i>k</i><sub>2</sub>,...,±<i>k</i><sub>q/2</sub>} or {±<i>k</i><sub>1</sub>,±<i>k</i><sub>2</sub>,...,±<i>k</i><sub>q-1/2</sub>}∪{<i>k</i><sub>q+1/2</sub>} according as <i>q</i> is even or odd. A graph with a pair sum labeling is called a pair sum graph. In this paper we investigate the pair sum labeling behavior of some trees which are derived from stars and bistars. Finally, we show that all trees of order nine are pair sum graphs.
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