Equitably strong nonsplit equitable domination in graphs

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-4497

Keywords:

Equitable domination, Split domination, Strong non - split domination

Abstract

In a simple, finite and undirected graph G with vertex set V and edge set E, Prof. Sampathkumar defined degree equitability among vertices of G. Two vertices u and v are said to be degree equitable if |deg(u) − deg(v)| ≤ 1. Equitable domination has been defined and studied in [7]. V.R.Kulli and B.Janakiram defined strong non - split domination in a graph [12]. In this paper, the equitable version of this new type of domination is studied

Author Biographies

P. Nataraj, The Madura College.

Dept. of Mathematics.

R. Sundareswaran, Sri Sivasubramaniya Nadar College of Engineering.

Dept. of Mathematics.

V. Swaminathan, Saraswathi Narayanan College.

Ramanujan Research Center in Mathematics.

References

K. D. Dharmalingam, “Studies in graph theorey-equitable domination and Bottleneck domination,” Ph.D. Thesis, Madurai Kamaraj University, Madurai, 2006.

K. M. Dharmalingam, “A note on the equitable covering and equitable packing of a graph”, Bulletin of international mathematical virtual institute, vol. 3, pp. 21-27, 2013. [Online]. Available: https://bit.ly/3y8D5HQ

K. M. Dharmalingam, “Equitable associate graph of a graph”, Bulletin of international mathematical virtual institute, vol. 2, pp. 109-116, 2012. [Online]. Available: https://bit.ly/2VfpboM

] V. R. Kulli and B. Janakiram, “The strong non-split domination number of a graph”, International journal of management and systems, vol. 19, no. 2, pp. 145-156, 2003. [Online]. Available: https://bit.ly/3y5ciMt

V. R. Kulli and B. Janakiram, “The split domination number of a graph”, Graph theory notes of New York, vol. 32, pp. 16-19. [Online]. Available: https://bit.ly/3zN6VlF

W. Meyer, “Equitable coloring”, The American mathematical monthly, vol. 80, No. 8, pp. 920-922, 1973. https://doi.org/10.2307/2319405

V. Swaminathan and K. M. Dharmalingam, “Degree equitable domination in graphs”, Kragujevac journal of mathematics, vol. 35, no.1, pp. 191-197, 2011. [Online]. Available: https://bit.ly/3i3aLB5

Published

2021-04-27 — Updated on 2021-07-26

How to Cite

[1]
P. Nataraj, R. Sundareswaran, and V. Swaminathan, “Equitably strong nonsplit equitable domination in graphs”, Proyecciones (Antofagasta, On line), vol. 40, no. 4, pp. 989-999, Jul. 2021.

Issue

Section

Artículos