Some Results on Prime Labeling

In the present work we investigate some classes of graphs and disjoint union of some classes of graphs which admit prime labeling. We also investigate prime labeling of a graph obtained by identifying two vertices of two graphs. We also investigate prime labeling of a graph obtained by identifying two edges of two graphs. Prime labeling of a prism graph is also discussed. We show that a wheel graph of odd order is switching invariant. A necessary and sufficient condition for the complement of Wn to be a prime graph is investigated.

Cite this paper

Prajapati, U. and Gajjar, S. (2014) Some Results on Prime Labeling. Open Journal of Discrete Mathematics, 4, 60-66. doi: 10.4236/ojdm.2014.43009.

 [1] Gross, J. and Yellen, J. (2004) Handbook of Graph Theory, CRC Press, Boca Raton. [2] Burton, D.M. (2007) Elementary Number Theory. 6th Edition, Tata McGraw-Hill Publishing Company Limited, New Delhi. [3] Gallian, J.A. (2012) A Dynamic Survey of Graph Labeling. The Electronic Journal of Combinatorics, 19, # DS6. [4] Tout, A., Dabboucy, A.N. and Howalla, K. (1982) Prime Labeling of Graphs. National Academy Science Letters, 11, 365-368. [5] Fu, H.L. and Huang, K.C. (1994) On Prime Labellings. Discrete Mathematics, 127, 181-186. http://dx.doi.org/10.1016/0012-365X(92)00477-9 [6] Lee, S.M., Wui, I. and Yeh, J. (1988) On the Amalgamation of Prime Graphs. Bull. of Malaysian Math. Soc., 11, 59-67. [7] Deretsky, T., Lee, S.M. and Mitchem, J. (1991) On Vertex Prime Labelings of Graphs. In: Alvi, J., Chartrand, G., Oellerman, O. and Schwenk, A., Eds., Graph Theory, Combinatorics and Applications. Proceedings of the 6th International Conference Theory and Applications of Graphs, Wiley, New York, 359-369. [8] Vaidya, S.K. and Prajapati, U.M. (2011) Some Results on Prime and K-Prime Labeling. Journal of Mathematics Research, 3, 66-75. http://dx.doi.org/10.5539/jmr.v3n1p66 [9] Vaidya, S.K. and Prajapati, U.M. (2012) Some Switching Invariant Prime Graphs. Open Journal of Discrete Mathematics, 2, 17-20. http://dx.doi.org/10.4236/ojdm.2012.21004