Applying the (1,2)-pitchfork domination and it's inverse on some special graphs
Résumé
Let G be a finite simple and undirected graph without isolated vertices. For any non-negative integers j and k, a subset D of V is called a pitchfork dominating set if every vertex in D dominates at least j and at most k vertices of V - D. A subset D -1 of V - D is an inverse pitchfork dominating set if it is a dominating set. The pitchfork domination number of G, denoted by pf (G) is a minimum cardinality over all pitchfork dominating sets in G. The inverse pitchfork domination number of G, denoted by pf-1 (G) is a minimum cardinality over all inverse pitchfork dominating sets in G. In this paper, pitchfork dominations and it's inverse are applied when j = 1 and k = 2 on some standard graphs such as: tadpole graph, lollipop graph, lollipop flower graph , daisy graph and Barbell graph.
Téléchargements
Références
M. A. Abdlhusein and M. N. Al-Harere, Pitchfork domination and its inverse for complement graphs, Proceedings of IAM, 9, 1, 13-17, (2020). https://doi.org/10.1142/S1793830921500385
M. A. Abdlhusein and M. N. Al-Harere, New parameter of inverse domination in graphs, Indian Journal of Pure and Applied Mathematicse, (accepted to appear)(2020). https://doi.org/10.1007/s13226-021-00082-z
M. A. Abdlhusein and M. N. Al-Harere, Some modified types of pitchfork domination and its inverse, Boletim da Sociedade Paranaense de Matem'atica, (accepted to appear) (2020). https://doi.org/10.1142/S1793830921500385
M. A. Abdlhusein and M. N. Al-Harere, Doubly connected pitchfork domination and its inverse in graphs, TWMS J. App. Eng. Math., (accepted to appear) (2020). https://doi.org/10.1142/S1793830921500385
M. N. Al-Harere and M. A. Abdlhusein, Pitchfork domination in graphs, Discrete Mathematics, Algorithms and Applications, 12, 2, 2050025, (2020). https://doi.org/10.1142/S1793830920500251
M. N. Al-Harere and A. T. Breesam, Further results on bi-domination in graphs, AIP Conf. Proc., 2096, 1, 020013-020013-9, (2019). https://doi.org/10.1063/1.5097810
M. N. Al-Harere and P. A. Khuda Bakhash, Tadpole domination in graphs, Baghdad Science Journal, 15, 4, 466-471, (2018). https://doi.org/10.21123/bsj.15.4.466-471
M. N. Al-Harere and A. A. Omran, On binary operation graphs, Boletim da Sociedade Paranaense de Matem'atica, 38, 7, 59-67, (2020). https://doi.org/10.5269/bspm.v38i7.44282
I. A. Alwan, A. A. Omran, Domination polynomial of the composition of complete graph and star graph, J. Phys.: Conf. Ser., 1591 012048, (2020). https://doi.org/10.1088/1742-6596/1591/1/012048
A. Das, R. C. Laskar and N. J. Rad, On α-domination in graphs, Graphs and Combinatorics, 34, 1, 193-205, (2018). https://doi.org/10.1007/s00373-017-1869-1
Gallian J. A., A dynamic survey of graph labeling, the Electronic j. of combinatorics. (2019). https://doi.org/10.37236/27
F. Harary, Graph Theory, Addison-Wesley, Reading Mass, (1969). https://doi.org/10.21236/AD0705364
T. W. Haynes, M. A. Henning and P. Zhang, A survey of stratified domination in graphs, Discrete Mathematics, Netherlands 309, 5806- 5819, (2009). https://doi.org/10.1016/j.disc.2008.02.048
T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of domination in graphs, Marcel Dekker, Inc., New York, (1998).
T. W. Haynes, S. T. Hedetniemi and P.J. Slater, Domination in graphs -Advanced Topics Marcel Dekker Inc., (1998).
A. A. Jabor and A. A. Omran, Domination in discrete topology graph, AIP, third international conference of science (ICMS2019), 2183, 030006-1-030006-3, (2019). https://doi.org/10.1063/1.5136110
R. M. J. Jothi and A. Amutha, An investigation on some classes of super strongly perfect graphs, Applied Mathematical Sciences, 7, 65, 5806- 5819, (2013). https://doi.org/10.12988/ams.2013.34229
A. Khodkar, B. Samadi and H. R. Golmohammadi, (k, k, ' k'')−Domination in graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, 98, 343-349, (2016).
C. Natarajan, S. K. Ayyaswamy and G. Sathiamoorthy, A note on hop domination number of some special families of graphs, International Journal of Pure and Applied Mathematics, 119, 12, 14165-14171, (2018).
A. A. Omran and T. Swadi, Some properties of frame domination in graphs, Journal of Engineering and Applied Sciences, 12, 8882-8885, (2017).
O. Ore, Theory of Graphs, American Mathematical Society, Provedence, R.I., (1962).
M. S. Rahman, Basic graph theory, Springer, India, (2017). https://doi.org/10.1007/978-3-319-49475-3
Y. B. Venkatakrishnan and V. Swaminathan, Bipartite theory on neighbourhood dominating and global dominating sets of a graph, Boletim da Sociedade Paranaense de Matem'atica, 32, 1, 175-180, (2014). https://doi.org/10.5269/bspm.v32i1.15783
H. J. Yousif and A. A. Omran, The split anti fuzzy domination in anti fuzzy graphs, J. Phys.: Conf. Ser., 1591012054, (2020). https://doi.org/10.1088/1742-6596/1591/1/012054
X. Zhang, Z. Shao and H. Yang, The [a, b]−domination and [a, b]−total domination of graphs, Journal of Mathematics Research, 9, 3, 38-45, (2017). https://doi.org/10.5539/jmr.v9n3p38
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática
Ce travail est disponible sous la licence Creative Commons Attribution 4.0 International .
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
