Equitable eccentric domination in graphs

Authors

  • A Riyaz Ur Rehman PG & Research Department of Mathematics, Jamal Mohamed College(Affiliated to Bharathidasan University), Tiruchirappalli-620020, Tamil Nadu, India.
  • A Mohamed Ismayil

DOI:

https://doi.org/10.23755/rm.v47i0.802

Keywords:

Eccentricity, equitable domination number, equitable eccentric domination number.

Abstract

In this paper, we define equitable eccentric domination in graphs. An eccentric dominating set S ⊆ V (G) of a graph G(V, E) is called an equitable eccentric dominating set if for every v ∈ V − S there exist at least one vertex u ∈ V such that |d(v) − d(u)| ≤ 1 where vu ∈ E(G). We find equitable eccentric domination number γeqed(G) for most popular known graphs. Theorems related to γeqed(G) have been stated and proved.

References

A. Anitha, S. Arumugam, and E. Sampathkumar, "Degree equitable sets in a graph," International J. Math. Combin., vol. 3, pp. 32-47, 2009.

B. Basavanagoud, V. Kulli, and V. T. Vijay, "Equitable dominating graph," Int. J. of Mathematical Science & Engineering Applications, vol. 9, no. 2, pp. 109-114, 2015.

E. J. Cockayne and S. T. Hedetniemi, "Towards a theory of domination in graphs," Networks, vol. 7, no. 3, pp. 247-261, 1977.

K. Dharmalingam, "Equitable graph of a graph," Proyecciones (Antofagasta), vol. 31, no. 4, pp. 363-372, 2012.

F. Harary, "Graph theory," Narosa Publishing House, New Delhi, 2001.

T. W. Haynes, S. Hedetniemi, and P. Slater, "Fundamentals of domination in graphs," CRC press, 2013.

A. M. Ismayil and A. R. U. Rehman, "Accurate eccentric domination in graphs," Our Heritage, vol. 68, no. 4 (1), pp. 209-216, 2020.

A. M. Ismayil and A. R. U. Rehman, "Equal eccentric domination in graphs," Malaya Journal of Matematik (MJM), vol. 8, no. 1, pp. 159-162, 2020.

T. Janakiraman, M. Bhanumathi, and S. Muthammai, "Eccentric domination in graphs," International Journal of Engineering Science, Computing and Bio-Technology, vol. 1, no. 2, pp. 1-16, 2010.

M.-J. Jou, "Upper domination number and domination number in a tree," Ars Combinatoria, vol. 94, pp. 245-250, 2010.

O. Ore, "Theory of graphs," Providence, American Mathematical Society, 1962.

V. Swaminathan and K. M. Dharmalingam, "Degree equitable domination on graphs," Kragujevac journal of Mathematics, vol. 35, pp. 191-197, 2011.

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Published

2023-06-30

Issue

Vol. 47 (2023)

Section

Volume 47-2023

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