Prime cordial labeling of some wheel related graphs

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DOI:

https://doi.org/10.26637/mjm104/017

Abstract

A prime cordial labeling of a graph \(G\) with the vertex set \(V(G)\) is a bijection \(f: V(G) \rightarrow\{1,2,3, \ldots,|V(G)|\}\) such that each edge \(u v\) is assigned the label 1 if \(\operatorname{gcd}(f(u), f(v))=1\) and 0 if \(\operatorname{gcd}(f(u), f(v))>1\), then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1 . A graph which admits prime cordial labeling is called prime cordial graph. In this paper we prove that the gear graph \(G_n\) admits prime cordial labeling for \(n \geq 4\). We also show that the helm \(H_n\) for every \(n\), the closed helm \(C H_n\) (for \(n \geq 5\) ) and the flower graph \(F l_n\) (for \(n \geq 4\) ) are prime cordial graphs.

Keywords:

Prime cordial labeling, gear graph, helm, closed helm, flower graph

Mathematics Subject Classification:

05C78
  • Pages: 148-156
  • Date Published: 01-10-2013
  • Vol. 1 No. 04 (2013): Malaya Journal of Matematik (MJM)

L. W. Beineke and S. M. Hegde, Strongly multiplicative graphs, Discuss. Math. Graph Theory, 21(2001), 63-75. DOI: https://doi.org/10.7151/dmgt.1133

I. Cahit, Cordial Graphs, A weaker version of graceful and harmonious Graphs, Ars Combinatoria, 23(1987), 201-207.

J. A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, 19(2012), #DS6.

R. L. Graham and N. J. A. Sloane, On additive bases and harmonious graphs, SIAM J. Alg. Disc. Meth., 1(4)(1980), 382-404. DOI: https://doi.org/10.1137/0601045

J. Gross and J. Yellen, Graph Theory and its Applications, CRC Press, 1999.

Z. Liang and Z. Bai, On the odd harmonious graphs with applications, J. Appl. Math. Comput., 29(2009), 105-116. DOI: https://doi.org/10.1007/s12190-008-0101-0

R. Sridevi, K. Krishnaveni and S. Navaneethakrishnan, A novel watershed image segmentation technique using graceful labeling, International Journal of Mathematics and Soft Computing, 3(1)(2013), 69-78. DOI: https://doi.org/10.26708/IJMSC.2013.1.3.08

M. Sundaram, R. Ponraj and S. Somasundram, Prime Cordial Labeling of graphs, J. Indian Acad. Math., 27(2)(2005), 373-390.

S. K. Vaidya and P. L. Vihol, Prime cordial labeling for some graphs, Modern Applied Science, 4(8)(2010), 119-126. DOI: https://doi.org/10.5539/mas.v4n8p119

S. K. Vaidya and P. L. Vihol, Prime cordial labeling for some cycle related graphs, Int. J. of Open Problems in Computer Science and Mathematics, 3(5)(2010), 223-232.

S. K. Vaidya and N. H. Shah, Some New Families of Prime Cordial Graphs, J. of Mathematics Research, 3(4)(2011), 21-30. DOI: https://doi.org/10.5539/jmr.v3n4p21

S. K. Vaidya and N. H. Shah, Prime Cordial Labeling of Some Graphs, Open Journal of Discrete Mathematics, 2(2012), 11-16. DOI: https://doi.org/10.4236/ojdm.2012.21003

V. Yegnanaryanan and P. Vaidhyanathan, Some Interesting Applications of Graph Labellings, J. Math. Comput. Sci., 2(5) (2012), 1522-1531.

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Published

01-10-2013

How to Cite

S. K. Vaidya, and N. H. Shah. “Prime Cordial Labeling of Some Wheel Related Graphs”. Malaya Journal of Matematik, vol. 1, no. 04, Oct. 2013, pp. 148-56, doi:10.26637/mjm104/017.