One modulo three mean labeling of transformed trees
DOI:
https://doi.org/10.4067/S0716-09172016000300005Keywords:
Mean labeling, one modulo three graceful labeling, one modulo three mean labeling, one modulo three mean graphs, transformed tree, etiquetado medio, etiquetado elegante de módulo tres, etiquetado de módulo tres, grafos medios de módulo tresAbstract
A graph G is said to be one modulo three mean graph if there is an injective function φ from the vertex set of G to the set {a|0 ≤ a ≤ 3q— 2 and either a ≡ 0(mod 3) or a ≡ 1(mod 3)} where q is the number of edges G and φ induces a bijection φ* from the edge set of G to {a|1 ≤ a ≤ 3q — 2 and either a ≡ 1(mod 3)} given by
and the function φ is called one modulo three mean labeling of G. In this paper, we prove that the graphs T ° Kn, T ô K1,n, T ô Pn and T ô 2Pn are one modulo three mean graphs.
References
[1] J. A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, 17, #DS6, (2015).
[2] F. Harary, Graph Theory, Addison Wesley, Massachusetts, 1972.
[3] S. M. Hegde, and Sudhakar Shetty,On Graceful Trees, Applied Mathematics E- Notes, 2, pp. 192-197, (2002).
[4] P. Jeyanthi and A. Maheswari, One modulo three mean labeling of graphs, American Journal of Applied Mathematics and Statistics, 2(5), pp. 302—306, (2014).
[5] P. Jeyanthi, A. Maheswari and P. Pandiaraj, One Modulo Three Mean Labeling of Cycle Related Graphs, International Journal of Pure and Applied Mathematics, 103(4), pp. 625-633, (2015).
[6] P. Jeyanthi, A. Maheswari and P. Pandiaraj, On one modulo three mean labeling of graphs, Journal of Discrete Mathematical Science & Cryptography, 19:2, pp. 375-384, (2016).
[7] S. Somasundaram, and R.Ponraj, Mean labeling of graphs, National Academy Science Letters, 26, pp. 210—213, (2003).
[8] V. Swaminathan and C. Sekar, Modulo three graceful graphs, Proceed. National Conference on Mathematical and Computational Models, PSG College of Technology, Coimbatore, pp. 281—286, (2001).
[2] F. Harary, Graph Theory, Addison Wesley, Massachusetts, 1972.
[3] S. M. Hegde, and Sudhakar Shetty,On Graceful Trees, Applied Mathematics E- Notes, 2, pp. 192-197, (2002).
[4] P. Jeyanthi and A. Maheswari, One modulo three mean labeling of graphs, American Journal of Applied Mathematics and Statistics, 2(5), pp. 302—306, (2014).
[5] P. Jeyanthi, A. Maheswari and P. Pandiaraj, One Modulo Three Mean Labeling of Cycle Related Graphs, International Journal of Pure and Applied Mathematics, 103(4), pp. 625-633, (2015).
[6] P. Jeyanthi, A. Maheswari and P. Pandiaraj, On one modulo three mean labeling of graphs, Journal of Discrete Mathematical Science & Cryptography, 19:2, pp. 375-384, (2016).
[7] S. Somasundaram, and R.Ponraj, Mean labeling of graphs, National Academy Science Letters, 26, pp. 210—213, (2003).
[8] V. Swaminathan and C. Sekar, Modulo three graceful graphs, Proceed. National Conference on Mathematical and Computational Models, PSG College of Technology, Coimbatore, pp. 281—286, (2001).
Published
2017-03-23
How to Cite
[1]
P. Jeyanthi, A. Maheswari, and P. Pandiaraj, “One modulo three mean labeling of transformed trees”, Proyecciones (Antofagasta, On line), vol. 35, no. 3, pp. 277-289, Mar. 2017.
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