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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.36 no.1 Antofagasta mar. 2017

http://dx.doi.org/10.4067/S0716-09172017000100001 

Odd vertex equitable even labeling of graphs

 

P. Jeyanthi

Govindammal Aditanar

College for Women

A. Maheswari Kamaraj

College of Engineering and Technology

M. Vijayalakshmi

Dr. G. U. Pope College of Engineering

India 


ABSTRACT

In this paper, we introduce a new labeling called odd vertex equitable even labeling. Let G be a graph with p vertices and q edges and A = {1, 3,..., q} if q is odd or A = {1, 3,..., q + 1} if q is even. A graph G is said to admit an odd vertex equitable even labeling if there exists a vertex labeling f : V(G) → A that induces an edge labeling f * defined by f * (uv) = f (u) + f (v) for all edges uv such thatfor all a and b in A, |vf (a) —vf (b)| ≤ 1 and the induced edge labels are 2, 4,..., 2q where vf (a) be the number of vertices v with f (v) = a for a ∈ A. A graph that admits odd vertex equitable even labeling is called odd vertex equitable even graph. We investigate the odd vertex equitable even behavior of some standard graphs.

Keywords : Mean labeling; odd mean labeling; k-equitable labeling; vertex equitable labeling; odd vertex equitable even labeling; odd vertex equitable even graph.

AMS Subject Classification : 05C78.


REFERENCES

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[7]    G. Sethuraman and P. Selvaraju, Gracefulness of Arbitrary Super Subdivision of Graphs, Indian J. Pure Appl. Math., 32 (7), pp. 1059-1064, (2001).         [ Links ]

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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: bala_nithin@yahoo.co.in

M.Vijayalakshmi

Department of Mathematics

Dr. G. U. Pope College of Engineering

Sawyerpuram, Tamilnadu,

India

e-mail: vijLmac@rediffmail.com

Received : January 2016. Accepted : May 2016

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