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A note on Roman $k$-tuple domination number | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 23، دوره 7، شماره 2، اسفند 2022، صفحه 273-274 اصل مقاله (275.56 K) | ||
| نوع مقاله: Short notes | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.27350.1242 | ||
| نویسندگان | ||
| Noor A'lawiah Abd Aziz1؛ Nader Jafari Rad* 2 | ||
| 1Universiti Sains Malaysia | ||
| 2Shahed University | ||
| چکیده | ||
| For an integer $k\geq 2$, a Roman $k$-tuple dominating function, (or just RkDF), in a graph $G$ is a function $f \colon V(G) \rightarrow \{0, 1, 2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least $k$ vertices $v$ for which $f(v) = 2$, and every vertex $u$ for which $f(u) \neq 0$ is adjacent to at least $k-1$ vertices $v$ for which $f(v) = 2$. The Roman $k$-tuple domination number of $G$ is the minimum weight of an RkDF in $G$. In this note we settle two problems posed in [Roman $k$-tuple Domination in Graphs, Iranian J. Math. Sci. Inform. 15 (2020), 101--115]. | ||
| کلیدواژهها | ||
| Dominating set؛ Roman domination؛ Total Roman dominating function؛ Roman k-tuple | ||
| مراجع | ||
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[1] H. Abdollahzadeh Ahangar, M.A. Henning, V. Samodivkin, and I.G. Yero, Total Roman domination in graphs, Appl. Anal. Discrete Math. 10 (2016), no. 2, 501–517.
[2] M. Chellali, N. Jafari Rad, S.M. Sheikholeslami, and L. Volkmann, Roman domination in graphs, Topics in Domination in Graphs, Springer, 2020, pp. 365–409.
[3] E.J. Cockayne, P.A. Dreyer Jr, S.M. Hedetniemi, and S.T. Hedetniemi, Roman domination in graphs, Discrete Math. 278 (2004), no. 1-3, 11–22.
[4] A P Kazemi, Roman k-tuple domination in graphs, Iranian Journal of Mathematical Sciences and Informatics 15 (2020), no. 2, 101–115.
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