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Domination number of middle graphs | ||
| Transactions on Combinatorics | ||
| دوره 12، شماره 2، شهریور 2023، صفحه 79-91 اصل مقاله (461.2 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2022.131151.1927 | ||
| نویسندگان | ||
| Farshad Kazemnejad1؛ Behnaz Pahlavsay2؛ Elisa Palezzato2؛ Michele Torielli* 3 | ||
| 1Department of Mathematics, School of Sciences, Ilam University, P.O.Box 69315-516, Ilam, Iran. | ||
| 2Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo 060-0810, Japan. | ||
| 3Hokkaido University, Department of Mathematics | ||
| چکیده | ||
| In this paper, we study the domination number of middle graphs. Indeed, we obtain tight bounds for this number in terms of the order of the graph G. We also compute the domination number of some families of graphs such as star graphs, double start graphs, path graphs, cycle graphs, wheel graphs, complete graphs, complete bipartite graphs and friendship graphs, explicitly. Moreover, some Nordhaus-Gaddum-like relations are presented for the domination number of middle graphs. | ||
| کلیدواژه‌ها | ||
| domination؛ middle graph؛ Nordhaus-Gaddum | ||
| مراجع | ||
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[1] M. Aouchiche and P. Hansen, A survey of Nordhaus-Gaddum type relations, Discrete Appl. Math., 161 (2013) 466–546. [2] J. A. Bondy and U. S. R. Murty, Graph theory, Graduate texts in mathematics, 244, Springer Science and Media, 2008. [3] T. Hamada and I. Yoshimura, Traversability and connectivity of the middle graph of a graph, Discrete Math., 14 (1976) 247–255. [4] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of domination in graphs, Monographs and Textbooks in Pure and Applied Mathematics, 208, Marcel Dekker, Inc., New York, 1998. [5] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Domination in Graphs: Advanced Topics, Marcel Dekker, New York, 1998. [6] M. A. Henning and A. Yeo, Total domination in graphs, Springer Monographs in Mathematics, 2013.
[7] F. Kazemnejad, B. Pahlavsay, E. Palezzato and M. Torielli, Total dominator coloring number of middle graphs, To appear in Discrete Mathematics, Algorithms and Applications. [8] F. Kazemnejad, B. Pahlavsay, E. Palezzato and M. Torielli, Total domination number of middle graphs, Electronic Journal of Graph Theory and Applications, 10 (2022) 275–288. [9] E. A. Nordhaus and J. W. Gaddum, On complementary graphs, Amer. Math. Monthly, 63 (1956) 175–177.
[10] B. Pahlavsay, E. Palezzato and M. Torielli, 3-tuple total domination number of rook’s graphs, Discuss. Math. Graph Theory, 42 (2022) 15–37. [11] B. Pahlavsay, E. Palezzato and M. Torielli, Domination for Latin square graphs, Graphs Combin., 37 (2021) 971–985. | ||
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