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Exact double domination in subdivision, Mycielskian and middle graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 اردیبهشت 1404 اصل مقاله (424.59 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.29949.2235 | ||
| نویسندگان | ||
| Ali Behtoei* ؛ Rozhin Zarifian | ||
| Department of Mathematics, Faculty of Science, Imam Khomeini International University, PO Box: 34148 - 96818, Qazvin, Iran | ||
| چکیده | ||
| An exact doubly dominating set (also called an efficient doubly dominating set in [F. Harary and T.W. Haynes, Double domination in graphs, Ars Combin. 55 (2000), 201–213]) for a graph $G=(V,E)$ is a subset $D$ of vertices such that each vertex of $G$ is dominated by exactly two vertices of $D$. In this paper we show that subdivision graphs admit exact doubly dominating sets under specific conditions, while Mycielskian and middle graphs do not. We provide some characterizations and we investigate the existence of exact doubly dominating sets for their complements. | ||
| کلیدواژه‌ها | ||
| Exact double domination؛ subdivision؛ middle؛ Mycielskian | ||
| مراجع | ||
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[1] S. Ahmadi, E. Vatandoost, and A. Behtoei, Domination number and identifying code number of the subdivision graphs, J. Algebraic Syst. 13 (2025), no. 2, 1–11. https://doi.org/10.22044/jas.2023.12257.1649
[2] D.W. Bange, A.E. Barkauskas, and P.J. Slater, Efficient dominating sets in graphs, SIAM, Philadelphia, PA, 1988.
[3] N. Biggs, Perfect codes in graphs, J. Combin. Theory (B) 15 (1973), no. 3, 289–296. https://doi.org/10.1016/0095-8956(73)90042-7
[4] B. Chaluvaraju, M. Chellali, and K.A. Vidya, Perfect codes in graphs, Australas. J. Comb. 48 (2010), 175–184.
[5] M. Chellali, A. Khelladi, and F. Maffray, Exact double domination in graph, Discuss. Math. Graph Theory 25 (2005), no. 3, 291–302.
[6] E.J. Cockayne, B. L. Hartnell, S.T. Hedetniemi, and R. Laskar, Perfect domination in graphs, J. Combin. Inform. System Sci. 18 (1993), 136–148.
[7] M.R. Fellows and M.N. Hoover, Perfect domination, Australas J. Comb. 3 (1991), 141–150.
[8] J.F. Fink and M.S. Jacobson, n-domination in graphs, Graph Theory with Appl. to Algorithms and Comp. Sci. (Y. Alavi, G. Chartrand, D.R. Lick, C.E. Wall, and L. Lesniak, eds.), John Wiley & Sons, Inc., United States, 1985, pp. 283–300.
[9] A. Ghalavand, S. Klavžar, M. Tavakoli, and I.G. Yero, On mixed metric dimension in subdivision, middle and total graphs, Quaestiones Math. 46 (2023), no. 12, 2517–2527. https://doi.org/10.2989/16073606.2023.2169206
[10] T. Hamada and I. Yoshimura, Traversability and connectivity of the middle graph of a graph, Discrete Math. 14 (1976), no. 3, 247–255. https://doi.org/10.1016/0012-365X(76)90037-6
[11] F. Harary and T.W. Haynes, Nordhaus-Gaddum inequalities for domination in graphs, Discrete Mathe. 155 (1996), no. 1-3, 99–105. https://doi.org/10.1016/0012-365X(94)00373-Q
[12] F. Harary and T.W. Haynes, Double domination in graphs, Ars Combin. 55 (2000), 201–213.
[13] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of domination in graphs, CRC Press, New York, 1998.
[14] F. Kazemnejad, B. Pahlavsay, E. Palezzato, and M. Torielli, Domination number of middle graphs, Trans. Comb. 12 (2023), no. 2, 79–91.
[15] R. Khoeilar, M. Kheibari, Z. Shao, and S.M. Sheikholeslami, Total $k$-rainbow domination subdivision number in graphs, Computer Sci. J. Moldova 28 (2020), no. 2, 152–169.
[16] R.Y. Salkhori, E. Vatandoost, and A. Behtoei, 2-rainbow domination number of the subdivision of graphs, Commun. Comb. Optim. to appear (2025), https://doi.org/10.22049/cco.2024.28850.1749 | ||
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