Author(s)

Raja Ponraj, Jeyaraj Vijaya Xavier Parthipan

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Let G be a (p,q) graph. An injective map f:V(G)→﹛±1,±2,...±p﹜is called a pair sum labeling if the induced edge function, f_e:E(G)→Z-﹛0﹜defined by f_e(uv)=f(u)+f(v) is one-one and f_e(E(G)) is either of the form {±k₁,±k₂,...,±k_q/2} or {±k₁,±k₂,...,±k_q-1/2}∪{k_q+1/2} according as q 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.

Path, Star, Bistar, Tree

R. Ponraj and J. Parthipan, "Further Results on Pair Sum Labeling of Trees," Applied Mathematics, Vol. 2 No. 10, 2011, pp. 1270-1278. doi: 10.4236/am.2011.210177.