The Regular Domination Number of Some Special Graphs

Authors

  • JYOTI RANI DEPARTMENT OF MATHEMATICS, MAHARSHI DAYANAND UNIVERSITY ROHTAK
  • Prof. Seema Mehra Department of Mathematics, MDU, Rohtak

Keywords:

Domination, Regular Domination, Regular Domination Number, Regular Dominating Set

Abstract

The purpose of this article is to illustrate the concept of regular domination on a variety of unique
graph types, including Complete graphs, Path graphs, Cycle graphs, Lollipop graphs, Barbell
graphs, Gear graphs, Petersen graphs, Helm graphs, Jellyfish graphs, Jewel graphs, and Complete
Bipartite graphs. We also determine the regular domination for specific operations, such as
the join of two graphs and the corona product of two graphs.

Downloads

Download data is not yet available.

References

A. A. Khalil, Determination and testing the domination numbers of helm graph,

web graph and levi graph using MATLAB. J. Edu. and Sci., 24(2), 2011. DOI:

33899/edusj.1999.58719

A. Brandstadt, V. B. Le and J. P. Spinrad. Graph classes : a survey, SIAM. Philadelphia, PA,

http://dx.doi.org/10.1137/1.9780898719796

A. Frendrup, M. A. Henning, B. Randerath and P. D. Vestergaard, An upper bound on the

domination number of graph with minimum degree 2, Discrete Mathematics. 309(639 -

(2009). DOI: 10.1016/j.disc.2007.12.080

A. Sugumaran and E. Jayachandran, Domination Number of Some Graphs, International

Journal of Scientific Development and Research, 3(11)(386-391).(2018).

https://www.ijsdr.org/papers/IJSDR1811068.pdf

C. Berge, Theory of graphs and applications. Translated by Alison Doig. Methuen Co. Ltd.

London, 1962. https://doi.org/10.1007/bf02478000

C. S. Nagabhushana, B. N. Kavitha and H. M. Chudamani, Split and Equitable Domination

of Some Special Graph, International Journal of Science and Technology and Engineering,

(2)(2017). https://www.ijste.org/articles/IJSTEV4I2037.pdf

D. A. Holton and J. Sheehan, The Petersen graph. Australian Mathematical Society Lecture

Notes 7, 1993. http://doi.org/10.1112/blms/27.1.89

E. Carmelito, Go and S. R. Canoy, Jr., Domination in Corona and Join of Graphs, International

Mathematical Forum. 6(16)(763-771).(2011).

J. Gallian, Dynamic survey of graph labeling. Electronic Journal of Combinatorics, DS6,

http://doi.org/10.37236/27

M. Herbster and M. Pontil, Prediction on a graph with a perception. Neural Information

Processing System Conference, 2006. http://doi.org/10.7551/mitpress/7503.003.0077

O.ore, Theory of graphs, Amer. Math. Soc. Colloq. Publication, R.I. (1962).

P. Prabakaran, N. Vinoth Kumar and N. Preethi, Regular Domination in Various Fuzzy

Graphs, Journal of Physics : Confernce Series. DOI: 10.1088/1742-6596/1947/1/012054

P. Z. Akbari, V. J. Kaneria and N. A. Parmar, Absolutely Mean Graceful Labelling of Jewel

Graph and Jelly fish Graph, International Journal of Mathematics Trends and Technology,

(1): 86- 93. (2022). doi : 10.14445/22315373/IJMTT-V68I1P510

R. S. Rajan, J. Anitha, I. Rajasingh (2015), Graphs with 2 - power domination number 2,

International journal of pure and applied mathematics.

S.R. Nayaka, Puttaswamy and S. Purushothama, Pendant Domination Polynomial of a

Graph, International Journal of Pure and Applied Mathematics ,117(11)(2017), 193-199.

https://acadpubl.eu/jsi/2017-117-11-14/articles/11/23.pdf

T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of domination in graphs,

Marcel Dekker, New York.(1998).

Published

24-04-2024

How to Cite

JYOTI RANI, & Prof. Seema Mehra. (2024). The Regular Domination Number of Some Special Graphs. Communications in Mathematics and Applications, 15(1). Retrieved from https://www.rgnpublications.com/journals/index.php/cma/article/view/2393

Issue

Section

Research Article