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On domination in an edge product hypergraphs | ||
| Journal of Hyperstructures | ||
| دوره 10، شماره 2، اسفند 2021، صفحه 108-117 اصل مقاله (313.58 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2021.2644 | ||
| نویسندگان | ||
| Kishor F. Pawar* 1؛ Megha M. Jadhav2 | ||
| 1Department of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, 425 001 M.S., India | ||
| 2Department of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University Jalgaon-425 001, India | ||
| چکیده | ||
| In this paper, we study domination in an edge product hypergraphs and found some results on it. It is proved that the unit edge in a unit edge product hypergraph is a dominating set of hypergraph H. Later, we obtained some results which are relatives of the Nordhaus-Gaddum theorem, regarding the sums and products of domination parameters in an edge product hypergraph and their compliments. | ||
| کلیدواژهها | ||
| Edge Product Hypergraph؛ Unit Edge Product Hypergraph؛ Nordhaus-Gaddum Theorem؛ Domination | ||
| مراجع | ||
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[1] B.D. Acharya, Domination in Hypergraphs, AKCE Int. J. Graphs Combin., 4(2) (2007), 117-126. [2] B.D. Acharya, Domination in hypergraphs: II-New Directions, Proc. Int. Conf. ICDM, (2008), 1-16. [3] C. Berge Theory of Graphs and its Applications, Methuen, London, (1962 ). [4] C. Berge, Graphs and Hypergraphs, North-Holland, Amsterdam, (1973). [5] C. Berge, Hypergraphs, Combinatorics of Finite Sets, North-Holland, Amsterdam, (1989). [6] Bibin K. Jose, Zs. Tuza, Hypergraph Domination and Strong Independence, Appl. Anal. Discrete Math., 3 (2009), 347358. [7] Haynes T.W., Hedetniemi S.T. and Slater P.J. Domination in Graphs-Advanced Topics, New York : Dekker, (1998). [8] Haynes T.W., Hedetniemi S.T. and Slater P.J. Fundamentals of Domination in Graphs, New York: Dekker (1998). [9] Megha M. Jadhav and Kishor F. Pawar, On Edge Product Hypergraphs, Journal of Hyperstructures, 10(1) (2021), 1-12. [10] F. Jaeger and C. Payan, Relations du type Nordhaus-Gaddum pour le nombre d absorption dun graphe simple, C.R. Acad. Sci., Paris, 274 (1972), 728730. [11] E. A. Nordhaus and J. W. Gaddum, On complementary Graphs, Amer. Math. Monthly, 63 (1956), 175177. [12] O. Ore, Theory of Graphs, Amer. Math. Soc. Trans., Vol. 38 Amer. Math. Soc., providence, RI, (1962), 206-212. | ||
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