Further Results on Pair Sum Labeling of Trees

Raja Ponraj, Jeyaraj Vijaya Xavier Parthipan

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DOI: 10.4236/am.2011.210177                

Abstract

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.

Keywords

Path, Star, Bistar, Tree

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. Ponraj and J. V. X. Parthipan, “Pair Sum Labeling of Graphs,” The Journal of Indian Academy of Mathematics, Vol. 32, No. 2, 2010, pp. 587-595.
[2]	R. Ponraj, J. V. X. Parthipan and R. Kala, “Some Results on Pair Sum Labeling,” International Journal of Mathematical Com-binatorics, Vol. 4, 2010, pp. 53-61.
[3]	R. Ponraj, J. V. X. Parthipan and R. Kala, “A Note on Pair Sum Graphs,” Journal of Scientific Research, Vol. 3, No. 2, 2011, pp. 321-329. doi:10.3329/jsr.v3i2.6290
[4]	F. Harary, “Graph Theory,” Narosa Pub-lishing House, New Delhi, 1998.
[5]	R. Ponraj, J. V. X. Parthipan and R. Kala, “Pair Sum Labeling of Some Trees,” The Journal of Indian Academy of Mathematics (Communicated), in Press.