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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.35 no.3 Antofagasta Sept. 2016

http://dx.doi.org/10.4067/S0716-09172016000300005 

 

One modulo three mean labeling of transformed trees

 

P. Jeyanthi

Govindammal Aditanar College for Women, India

A. Maheswari 

Kamaraj College of Engineering and Technology, India

P. Pandiaraj

Kamaraj College of Engineering and Technology, India


ABSTRACT

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 2Pare one modulo three mean graphs.

Keywords : Mean labeling, one modulo three graceful labeling, one modulo three mean labeling, one modulo three mean graphs, transformed tree.

AMS Subject Classification : 05C78.


REFERENCES

[1]    J. A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, 17, #DS6, (2015).         [ Links ]

[2]    F. Harary, Graph Theory, Addison Wesley, Massachusetts, 1972.         [ Links ]

[3]    S. M. Hegde, and Sudhakar Shetty,On Graceful Trees, Applied Mathematics E- Notes, 2, pp. 192-197, (2002).         [ Links ]

[4]    P. Jeyanthi and A. Maheswari, One modulo three mean labeling of graphs, American Journal ofApplied Mathematics and Statistics, 2(5), pp. 302-306, (2014).         [ Links ]

[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).         [ Links ]

[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).         [ Links ]

[7]    S. Somasundaram, and R.Ponraj, Mean labeling of graphs, National Academy Science Letters, 26, pp. 210-213, (2003).         [ Links ]

[8]    V. Swaminathan and C. Sekar, Modulo three graceful graphs, Pro-ceed. National Conference on Mathematical and Computational Mod-els, PSG College of Technology, Coimbatore, pp. 281-286, (2001).         [ Links ]


Received : December 2015. Accepted : February 2016

 

P. Jeyanthi
Research Centre
Department of Mathematics
 Govindammal Aditanar College for Women
 Tiruchendur-628 215, Tamilnadu,

India
e-mail: jeyajeyanthi@rediffmail.com

A. Maheswari
Department of Mathematics
Kamaraj College of Engineering and Technology
Virudhunagar, Tamilnadu,
India
e-mail: ttfamily bala_nithin@yahoo.co.in

P. Pandiaraj
Department of Mathematics
Kamaraj College of Engineering and Technology
Virudhunagar, Tamilnadu,
India
e-mail : pandiaraj0@gmail.com

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