Prime Cordial Labeling of Some Graphs

Samir K. Vaidya, Nirav H. Shah

.

DOI: 10.4236/ojdm.2012.21003                

Abstract

In this paper we prove that the split graphs of K_1,n and B_n,n are prime cordial graphs. We also show that the square graph of B_n,n is a prime cordial graph while middle graph of P_n is a prime cordial graph for n≥4 . Further we prove that the wheel graph W_n admits prime cordial labeling for n≥8.

Keywords

Prime Cordial Labeling; Split Graph; Square Graph; Middle Graph

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. Gross and J. Yellen, “Graph Theory and Its Applications,” CRC Press, Boca Raton, 1999.
[2]	L. W. Beineke and S. M. Hegde, “Strongly Multiplicative Graphs,” Discussiones Mathematicae Graph Theory, Vol. 21, 2001, pp. 63-75.
[3]	J. A. Gallian, “A Dynamic Survey of Graph Labeling,” The Electronic Journal of Combinatorics, Vol. 17, 2010, DS6. http://www.combinatorics.org/Surveys/ds6.pdf
[4]	I. Cahit, “Cordial Graphs: A Weaker Version of Graceful and Harmonious Graphs,” Ars Combinatoria, Vol. 23, 1987, pp. 201-207.
[5]	M. Sundaram, R. Ponraj and S. Somasundram, “Prime Cordial Labeling of Graphs,” Journal of the Indian Academy of Mathematics, Vol. 27, No. 2, 2005 , pp. 373- 390.
[6]	S. K. Vaidya and P. L. Vihol, “Prime Cordial Labeling for Some Graphs,” Modern Applied Science, Vol. 4, No. 8, 2010, pp. 119-126.
[7]	S. K. Vaidya and P. L. Vihol, “Prime Cordial Labeling for Some Cycle Related Graphs,” International Journal of Open Problems in Computer Science and Mathematics, Vol. 3, No. 5, 2010, pp. 223-232.
[8]	S. K. Vaidya and N. H. Shah, “Some New Families of Prime Cordial Graphs,” Journal of Mathematics Research, Vol. 3, No. 4, 2011, pp. 21-30. doi:10.5539/jmr.v3n4p21