Vertex Bimagic Total Labeling for Graphs

R. Senthil Amutha; N. Murugesan

doi:https://doi.org/10.14445/22315373/IJMTT-V36P531

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 36 | Number 4 | Year 2016 | Article Id. IJMTT-V36P531 | DOI : https://doi.org/10.14445/22315373/IJMTT-V36P531

Vertex Bimagic Total Labeling for Graphs

R. Senthil Amutha, N. Murugesan

Abstract

t. A vertex magic total labeling on a graph with v vertices and e edges is a one to one map taking the vertices and edges onto the integers with the property that the sum of the label on the vertex and the labels of its incident edges is a constant, independent of the choice of the vertex. A graph with vertex magic total labeling with two constants or is called a vertex bimagic total labeling. The constants and are called magic constants. In this paper we have found that the star graphs for all , cycle when is even, crown graphs , kite graph for odd , wheel graph ,the fan graph admits vertex bimagic total labeling. It has been proved that the star graphs has vertex bimagic total labeling for all , but does not have vertex magic total labeling for . It has also been discussed that the vertex bimagic total labeling of Petersen graphs and when is a multiple of 4, . Also the extremities of bimagic constants in vertex bimagic total labeling graphs has also been discussed in this paper.

Keywords

vertex bimagic total labeling, bimagic constants.

References

[1] J. Baskar Babujee, Bimagic labeling in path graphs, The Mathematics Education, Volume 38, No.1, pp. 12-16, 2004.
[2] J. Baskar Babujee and V. Vishnu Priya, Edge Bimagic labeling in graphs, Acta Ciencia Indica, Vol. XXXIM, No. 3, pp. 741, 2005.
[3] S. Karthikeyan, S. Navaneethakrishnan , and R. Sridevi , Total Fibonacci irregular labeling of some star graphs, International Journal of Mathematics and Soft computing, Vol.5, No.1, pp. 73-78, 2015.
[4] K. Manimekalai and K. Thirusangu, Pair Sum Labeling of Some Special Graphs, International Journal of Computing Algorithm Vol 02, pp. 251-256, Oct 2013.
[5] N. Murugesan, R. SenthilAmutha ,Vertex Bimagic Total Labeling For Bistar , International Journal of Scientific and Innovative Mathematical Research (IJSIMR), Volume 2, Issue 9, pp. 764-769, September 2014.
[6] S.K. Vaidya and Lekha Biju Kumar, Some new families of mean labeling , Journal of Mathematics research , Vol.2, No. 3, Aug 2010.
[7] V. Vishnu Priya, K. Manimegalai & J. Baskar Babujee, Edge bimagic labeling for some trees, Acta ciencia Indica, Vol XXXVM.No.2,pp. 569, 2009.
[8] W.D. Wallis, E.T. Baskoro, Mirka Miller and Slamin, Edge-magic total labeling, Australasian Journal of Combinatorics 22pp.177-190, 2000.
[9] W.D. Wallis, Magic Graphs, Birkhauser, Boston MA 2001.

Citation :

R. Senthil Amutha, N. Murugesan, "Vertex Bimagic Total Labeling for Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 36, no. 4, pp. 225-232, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V36P531