Total edge irregularity strength of disjoint union of double wheel graphs

Authors

  • P. Jeyanthi Govindammal Aditanar College for Women.
  • A. Sudha Wavoo Wajeeha Women’s College of Arts & Science.

DOI:

https://doi.org/10.4067/S0716-09172016000300003

Keywords:

Irregularity strength, total edge irregularity strength, edge irregular total labeling, disjoint union of double wheel graphs, fuerza de irregularidad, fuerza total de irregularidad, etiquetado irregular total de borde

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.

Author Biographies

P. Jeyanthi, Govindammal Aditanar College for Women.

Research Centre, Department of Mathematics.

A. Sudha, Wavoo Wajeeha Women’s College of Arts & Science.

Department of Mathematics.

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).

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

[3] J.Ivanco, S.Jendrol, Total edge irregularity strength of trees, Discussiones Math. Graph Theory, 26, pp. 449-456, (2006).

[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).

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

Published

2017-03-23

How to Cite

[1]
P. Jeyanthi and A. Sudha, “Total edge irregularity strength of disjoint union of double wheel graphs”, Proyecciones (Antofagasta, On line), vol. 35, no. 3, pp. 251-262, Mar. 2017.

Issue

Section

Artículos