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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

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

http://dx.doi.org/10.4067/S0716-09172016000300003 

 

Total edge irregularity strength of disjoint union of double wheel graphs

 

P. Jeyanthi

Govindammal Aditanar College for Women, India

A. Sudha

Wavoo Wajeeha Women’s College of Arts & Science, India


ABSTRACT

An edge irregular total k-labeling f : V ∪ E → {1, 2, 3,...,k} of a graph G = (V, E) is a labeling of vertices and edges of G in such a way thatfor any two different edges uv and u'v' their weights f (u) + f (uv) + f (v) and f (u') + f (u'v') + f (v') are distinct. The total edge irregularity strength tes(G) is defined as the minimum k for which the graph G has an edge irregular total k-labeling. In this paper, we determine the total edge irregularity strength of disjoint union of p isomorphic double wheel graphs and disjoint union of p consecutive non-isomorphic double wheel graphs.

Keywords: Irregularity strength; total edge irregularity strength; edge irregular total labeling, disjoint union of double wheel graphs.

AMS Classification (2010): 05C78.


REFERENCES

[1]    A. Ahmad and M.Baca, and Muhammad Numan, On irregularity strength of the disjoint union of friendship graphs, Electronic Journal of Graph Theory and Applications, 11 (2), pp. 100-108, (2013).         [ Links ]

[2]    M.Baca,S.Jendrol, M. Miller and J. Ryan, On irregular total la-bellings, Discrete Math., 307, pp. 1378-1388, (2007).         [ Links ]

[3]    JJvanco,S.Jendrol, Total edge irregularity strength of trees, Discus-siones Math. Graph Theory, 26, pp. 449-456, (2006).         [ Links ]

[4]    M.K.Siddiqui,A.Ahmad,M.F.Nadeem,Y.Bashir, Total edge irregularity strength of the disjoint union of sun graphs, International Journal of Mathematics and Soft Computing 3 (1), pp. 21-27, (2013).         [ Links ]

[5]    P. Jeyanthi and A. Sudha, Total Edge Irregularity Strength ofDisjoint Union of Wheel Graphs, Electron. Notes in Discrete Math., 48, pp. 175-182, (2015).         [ Links ]


Received : October 2015. Accepted : March 2016

 

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

India
e-mail: jeyajeyanthi@rediffmail.com

A. Sudha
Department of Mathematics
Wavoo Wajeeha Women’s College of Arts & Science,
Kayalpatnam -628 204,Tamil Nadu, India
 e-mail: sudhathanalakshmi@gmail.com

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