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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 52 | Number 4 | Year 2017 | Article Id. IJMTT-V52P531 | DOI : https://doi.org/10.14445/22315373/IJMTT-V52P531

k-Harmonic Mean Labeling of Some Graphs


Dr. M. Tamilselvi, N. Revathi
Abstract

Somasundaram and Ponraj [12] have introduced the notion of mean labeling of graphs. R. Ponraj and D. Ramya introduced Super mean labeling of graphs in [5]. S. Somasundaram and S.S. Sandhya introduced the concept of Harmonic mean labeling in [6] and studied their behavior in [7,8,9]. In this paper, we introduce the concept of kharmonic mean labeling and we investigate k-harmonic mean labeling of some graphs.

Keywords
Harmonic mean labeling, harmonic mean graph, k-harmonic mean labeling, k-harmonic mean graph.
References

[1] J. A. Gallian, “A Dynamic Survey of Graph Labeling”, The Electronic Journal of CombinatoricsDS6, 2016.
[2] B. Gayathri and M. Tamilselvi, “k-super mean labeling of some trees and cycle related graphs”, Bulletin of Pure and Applied Sciences, Volume 26E(2) (2007) 303-311.
[3] F. Harary, 1998, “Graph theory”, Narosa Publishing House Reading, New Delhi.
[4] P. Jeyanthi and D. Ramya “Super mean labeling of some classes of graphs” International journal of Math.Combin.Vol. 1 (2012), 83-91.
[5] D .Ramya, R.Ponraj and P.Jeyanthi, “Super Mean Labeling of Graphs”, Ars Combinatoria, Vol.112(2013), 65-72.
[6] S.S. Sandhya, S. Somasundaram and R. Ponraj, “Some results on Harmonic mean graphs”, International Journal of Contemporary Mathematical Sciences Vol.7(2012), No. 4, 197-208.
[7] S. S. Sandhya, S. Somasundaram and R. Ponraj, “Some more results on Harmonic mean graphs”, Journal of Mathematics Research, Vol.4(2012), No.1, 21-29.
[8] S. S. Sandhya, S. Somasundaram and R. Ponraj, “Harmonic mean labeling of some Cycle Related Graphs”, International Journal of Mathematical Analysis, Vol.6(2012), No.40, 1997-2005.
[9] S. S. Sandhya and C. David Raj, “Some results on Super Harmonic mean graphs”, International Journal of Mathematics Trends and Technology – Volume 6 – February 2014.
[10] S. S. Sandhya, E. Ebin Raja Merly and B. Shiny, “Some more results on super geometric mean labeling”, International Journal of Mathematical Archive-6(1), 2015, 121-132.
[11] Selvam Avadayappan and R. Vasuki, “New families of mean graphs”, International J. Math. combin.Vol.2(2010), 68-80.
[12] S. Somasundaram and R. Ponraj, “Mean labeling of graphs”, National Academy of Science letters Vol. 26(2003), 210-213.
[13] M. Tamilselvi, A study in Graph Theory – “Generalization of super mean labeling”, Ph.D. Thesis, Vinayaka Mission University, Salem, August (2011).
[14] M. Tamilselvi and N. Revathi, “k-Super harmonic mean labeling of some graphs”, Aryabhatta journal of mathematics and informatics, Vol.9, Issue-01 (Jan-June 2017), 779-787.
[15] M. Tamilselvi and N. Revathi, “k-super harmonic mean labeling of some disconnected graphs”, International journal of recent innovation in engineering and technology, Vol.2, Issue 8, August 2017 (27-32).
[16] R. Vasuki and A. Nagarajan, “Further results on mean graphs”, Scientia Manga, 6(3)(2010), 1-14.

Citation :

Dr. M. Tamilselvi, N. Revathi, "k-Harmonic Mean Labeling of Some Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 52, no. 4, pp. 216-222, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V52P531

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