The Arrow Domination of Some Generalized Graphs

Authors

DOI:

https://doi.org/10.26713/cma.v14i1.1969

Keywords:

Domination, Arrow domination, Arrow domination number, Arrow dominating set

Abstract

The aim of this article is to apply the concept of arrow domination defined by Radhi et al. (The arrow domination in graphs, International Journal of Nonlinear Analysis and Applications 12(1) (2021), 473 – 480) on some generalized graphs like Friendship graph or Fan graph, Gear graph, Helm graph, Flower graph, Sunflower graph, Triangular snake graph, Double triangular snake graph, Petersen graph, Dragon graph, Lollipop graph and Barbell graph.

Downloads

Download data is not yet available.

References

C. Berge, Theory of Graphs and Applications, translated by A. Doig, John Wiley & Sons, Inc., New York, ix + 247 pages (1962).

A. Brandstädt, V. B. Le and J. P. Spinrad, Graph Classes: A Survey, Discrete Mathematics and Applications series, SIAM, Philadelphia, PA, xi + 295 pages (1999), DOI: 10.1137/1.9780898719796.

J. A. Gallian, A dynamic survey of graph labeling, Electronic Journal of Combinatorics DS6 (2022), 623 pages, URL: 10.37236/27.

T. W. Haynes, S. Hedetniemi and P. Slater, Fundamentals of Domination in Graphs, 1st Edition, CRC Press, Boca Raton, 464 pages (1998), DOI: 10.1201/9781482246582.

M. Herbster and M. Pontil, Prediction on a graph with a perceptron, in: Advances in Neural Information Processing Systems: Proceedings of the 2006 Conference, B. Schölkopf, J. Platt and T. Hofmann, The MIT Press, (2007), DOI: 10.7551/mitpress/7503.003.0077.

D. A. Holton and J. Sheehan, The Petersen Graph, Cambridge University Press, Cambridge (1993), DOI: 10.1017/CBO9780511662058.

K. Kavitha and N. G. David, Dominator coloring of some classes of graphs, International Journal of Mathematical Archive 3(11) (2012), 3954 – 3957, URL: http://www.ijma.info/index.php/ijma/article/view/1713/1005.

A. A. Khalil, Determination and testing the domination numbers of Helm graph, web graph and levi graph using MATLAB, Journal of Education and Science 24(2) (2011), 103 – 116, DOI: 10.33899/edusj.1999.58719.

K. B. Murthy, The end equitable domination in graph, Journal of Computer and Mathematical Sciences 6(10) (2015), 552 – 563.

S. J. Radhi, M. A. Abdlhusein and A. E. Hashoosh, The arrow domination in graphs, International Journal of Nonlinear Analysis and Applications 12(1) (2021), 473 – 480, DOI: 10.22075/ijnaa.2021.4826.

N. Senthurpriya and S. Meenakshi, Independent domination number for some special types of snake graph, Journal of Physics: Conference Series 1818(1) (2021), 012218, DOI: 10.1088/1742-6596/1818/1/012218.

Downloads

Published

09-05-2023
CITATION

How to Cite

Dipshi, & Mehra, S. (2023). The Arrow Domination of Some Generalized Graphs. Communications in Mathematics and Applications, 14(1), 333–347. https://doi.org/10.26713/cma.v14i1.1969

Issue

Vol. 14 No. 1 (2023)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.