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Remarks on the restrained Italian domination number in graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 15، دوره 8، شماره 1، خرداد 2023، صفحه 183-191 اصل مقاله (359.78 K) | ||
| نوع مقاله: Short notes | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.27471.1269 | ||
| نویسنده | ||
| Lutz Volkmann* | ||
| RWTH Aachen University | ||
| چکیده | ||
| Let $G$ be a graph with vertex set $V(G)$. An Italian dominating function (IDF) is a function $f:V(G)\longrightarrow \{0,1,2\}$ having the property that that $f(N(u))\geq 2$ for every vertex $u\in V(G)$ with $f(u)=0$, where $N(u)$ is the neighborhood of $u$. If $f$ is an IDF on $G$, then let $V_0=\{v\in V(G): f(v)=0\}$. A restrained Italian dominating function (RIDF) is an Italian dominating function $f$ having the property that the subgraph induced by $V_0$ does not have an isolated vertex. The weight of an RIDF $f$ is the sum $\sum_{v\in V(G)}f(v)$, and the minimum weight of an RIDF on a graph $G$ is the restrained Italian domination number. We present sharp bounds for the restrained Italian domination number, and we determine the restrained Italian domination number for some families of graphs. | ||
| کلیدواژهها | ||
| Italian domination؛ restrained Italian domination؛ restrained domination | ||
| مراجع | ||
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[1] H. Abdollahzadeh Ahangar, M. Chellali, M. Hajjari, and S.M. Sheikholeslami, Further progress on the total Roman {2}-domination number of graphs, Bull. Iranian Math. Soc. (In press).
[2] H. Abdollahzadeh Ahangar, M. Chellali, S.M. Sheikholeslami, and J.C. Valenzuela-Tripodoro, Total Roman {2}-dominating functions in graphs, Discuss. Math. Graph Theory (In press).
[3] H. Abdollahzadeh Ahangar and S.R. Mirmehdipour, Bounds on the restrained Roman domination number of a graph, Commun. Comb. Optim. 1 (2016), no. 1, 75–82.
[4] F. Azvin and N. Jafari Rad, Bounds on the double Italian domination number of a graph, Discuss. Math. Graph Theory (In press).
[5] F. Azvin, N. Jafari Rad, and L. Volkmann, Bounds on the outer-independent double Italian domination number, Commun. Comb. Optim. 6 (2021), no. 1, 123–136.
[6] M. Chellali, T.W. Haynes, S.T. Hedetniemi, and A. MacRae, Roman {2}-domination, Discrete Appl. Math. 204 (2016), 22–28.
[7] M. Chellali, N. Jafari Rad, S.M. Sheikholeslami, and L. Volkmann, Roman domination in graphs, Topics in Domination in Graphs (T.W. Haynes, S.T. Hedetniemi, and M.A. Henning, eds.), Springer, Berlin/Heidelberg, 2020, pp. 365–409.
[8] M. Chellali, N. Jafari Rad, S.M. Sheikholeslami, and L. Volkmann, A survey on Roman domination parameters in directed graphs, J. Combin. Math. Comb. Comput. 151 (2020), 141–171.
[9] M. Chellali, N. Jafari Rad, S.M. Sheikholeslami, and L. Volkmann, Varieties of Roman domination II, AKCE Int. J. Graphs Comb. 17 (2020), no. 3, 966–984.
[10] M. Chellali, N. Jafari Rad, S.M. Sheikholeslami, and L. Volkmann, Varieties of Roman domination, Structures of Domination in Graphs (T.W. Haynes, S.T. Hedetniemi, and M.A. Henning, eds.), Springer, Berlin/Heidelberg, 2021, pp. 273–307.
[11] 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.
[12] G.S. Domke, J.H. Hattingh, S.T. Hedetniemi, R.C. Laskar, and L.R. Markus, Restrained domination in graphs, Discrete Math. 203 (1999), no. 1-3, 61–69.
[13] J.H. Hattingh and E.F. Joubert, Restrained and total restrained domination in graphs, Topics in Domination in Graphs (T.W. Haynes, S.T. Hedetniemi, and M.A. Henning, eds.), Springer, 2020, pp. 129–150.
[14] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York, 1998.
[15] D.A. Mojdeh and L. Volkmann, Roman {3}-domination (double Italian domination), Discrete Appl. Math. 283 (2020), 555–564.
[16] E.A. Nordhaus and J.W. Gaddum, On complementary graphs, Amer. Math. Monthly 63 (1956), no. 3, 175–177.
[17] R.L. Pushpam and S. Padmapriea, Restrained Roman domination in graphs, Trans. Comb. 4 (2015), no. 1, 1–17.
[18] B. Samadi, M. Alishahi, I. Masoumi, and D.A. Mojdeh, Restrained Italian domination in graphs, RAIRO-Oper. Res. 55 (2021), no. 2, 319–332.
[19] F. Siahpour, H. Abdollahzadeh Ahangar, and S.M. Sheikholeslami, Some progress on the restrained Roman domination, Bull. Malays. Math. Sci. Soc. 44 (2021), no. 2, 733–751.
[20] L. Volkmann, Restrained double Italian domination in graphs, Commun. Comb. Optim. (In press). | ||
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