Variant Domination Types for a Complete h-ary Tree
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Abstract
Graph is a tool that can be used to simplify and solve network problems. Domination is a typical network problem that graph theory is well suited for. A subset of nodes in any network is called dominating if every node is contained in this subset, or is connected to a node in it via an edge. Because of the importance of domination in different areas, variant types of domination have been introduced according to the purpose they are used for. In this paper, two domination parameters the first is the restrained and the second is secure domination have been chosn. The secure domination, and some types of restrained domination in one type of trees is called complete ary tree are determined.
Received 30/5/2019
Accepted 20/10/2020
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References
Claude B. The theory of graphs and its applications. London: Methuen. New York: Wiley.1962.
Frank H. Graph theory. London: Addison-Wesley. 1969.
Oystein O. Theory of graphs. Providence. RI: American Mathematical Society. 1962.
Teresa WH, Stephen TH, Peter JS. Fundamentals of domination in graphs. New York: Marcel Dekkar. 1998.
Hedetneimi ST , Laskar R .Topics in domination in graphs. Discrete Math. 1990;88.
Al-Harere M N, Khuda Bakhash PA. Tadpole domination in graphs. Baghdad Sci. J. 2018; 15(4):466-471.
Al-Harere MN, Omran AA . Binary operation in graphs. Bol. Soc. Paran. Mat. (2020); 38 (7): 59–67.
Al-Harere MN, Abdlhusein MA. Pitchfork domination in graphs. Discrete Mathematics, Algorithm and Applications.2020; 12(2): 2050025.
Al-Harere MN, Breesam AT. Further results on bi-domination in graphs. AIP Conference Proceedings . 2019; 2096(1): 020013-1–020013-9.
Abdlhusein MA, Al-Harere MN. Pitchfork Domination and It's Inverse for Corona and Join Operations in Graphs .PIMS .2020; 1 (2): 51 – 55.
Abdlhusein MA, Al-Harere MN. Pitchfork Domination and It's Inverse for Complement graphs. Proceedings of IAM. 2020; 9(1):13-17.
Omran AA, Al Hwaeer H J. Modern roman domination in graphs .BJS (A). 2018; 36 (1): 45-54.
Jabour AA , Omran AA . Domination in discrete topology graph. AIP Conference Proceedings..2019; 2183(6): 030006.
Omran AA, Haneen H O. Hn domination in graphs. Baghdad Sci. J. 2019; 16(1):242-247.
Domke GS, Hattingh JH, Henning MA, Markus LR. Restrained domination in tress. Discrete Math. . 2000; 211(3): 1-9.
Nicanor T, Sergio R, Canoy J. Independent restrained domination in graphs. Appl. Math. Sci. 2014; 8 (121): 6033 – 6038.
Hattingh JH, Jonck E, Joubert EJ, Plummer AR . Total restrained domination in trees. Discrete Math. 2007; 307: 1643-1650.
Houcine BM, Mustapha.C. On secure domination in graphs, Information Processing. Letters.2015; 115(10):786-790.
Burger AP, de Villiers A, van Vuuren JH.On Minimum secure dominating sets of graphs. QUAEST MATH. 2016; 39(2):189-202.