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Further results on maximal rainbow domination number | ||
| Transactions on Combinatorics | ||
| مقاله 29، دوره 9، شماره 4، اسفند 2020، صفحه 201-210 اصل مقاله (249.33 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2020.120014.1684 | ||
| نویسنده | ||
| Hossein Abdollahzadeh Ahangar* | ||
| Department of Mathematics, Babol Noshirvani University of Technology, Babol, I.R. Iran | ||
| چکیده | ||
| A 2-rainbow dominating function (2RDF) of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set $\{1,2\}$ such that for any vertex $v\in V(G)$ with $f(v)=\emptyset$ the condition $\bigcup_{u\in N(v)}f(u)=\{1,2\}$ is fulfilled, where $N(v)$ is the open neighborhood of $v$. A maximal 2-rainbow dominating function of a graph $G$ is a $2$-rainbow dominating function $f$ such that the set $\{w\inV(G)|f(w)=\emptyset\}$ is not a dominating set of $G$. The weight of a maximal 2RDF $f$ is the value $\omega(f)=\sum_{v\in V}|f (v)|$. The maximal $2$-rainbow domination number of a graph $G$, denoted by $\gamma_{m2r}(G)$, is the minimum weight of a maximal 2RDF of $G$. In this paper, we continue the study of maximal 2-rainbow domination {number} in graphs. Specially, we first characterize all graphs with large maximal 2-rainbow domination number. Finally, we determine the maximal $2$-rainbow domination number in the sun and sunlet graphs. | ||
| کلیدواژه‌ها | ||
| $2$-rainbow dominating function؛ $2$-rainbow domination number؛ maximal $2$-rainbow dominating function؛ maximal $2$-rainbow domination number | ||
| مراجع | ||
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[1] H. Abdollahzadeh Ahangar, J. Amjadi, N. Jafari Rad and V. Samodivkin, Total k-rainbow domination numbers in graphs, Commun. Comb. Optim., 3 (2018) 37–50. [2] H. Abdollahzadeh Ahangar, M. Khaibari, N. Jafari Rad and S. M. Sheikholeslami, Graphs with large total 2-rainbow domination number, Iran. J. Sci. Technol. Trans. A Sci., 42 (2018) 841–846. [3] H. Abdollahzadeh Ahangar, J. Amjadi, S.M. Sheikholeslami and D. Kuziak, Maximal 2-rainbow domination number of a graph, AKCE Int. J. Graphs Comb., 13 (2016) 157–164. [4] H. Abdollahzadeh Ahangar, H. Jahani, N. Jafari Rad, Rainbow edge domination numbers in graphs, Asian-Eur. J. Math., 13 (2020) (16 pages). [5] M. Chellali and N. Jafari Rad, On 2-rainbow domination and Roman domination in graphs, Australas. J. Combin., 56 (2013) 85–93. [6] M. Falahat, S. M. Sheikholeslami and L. Volkmann, New bounds on the rainbow domination subdivision number, Filomat, 28 (2014) 615–622. [7] B. Brešar, M. A. Henning and D. F. Rall, Rainbow domiantion in graphs, Taiwanese J. Math., 12 (2008) 213–225.
[8] B. Brešar and T. Kraner Šumenjak, On the 2-rainbow domination in graphs, Discrete Appl. Math., 155 (2007) 2394–2400. [9] C. D. Godsil and B. D. McKay, A new graph product and its spectrum, Bull. Austral. Math. Soc., 18 (1) (1978) 21–28. [10] T. W. Haynes, S. T. Hedetniemi and P. J. Slater (eds.), Domination in graphs: Advanced Topics, Marcel Dekker, Inc. New York, 1998. [11] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of domination in graphs, Marcel Dekker, Inc. New York, 1998. [12] Y. Wu and N. Jafari Rad, Bounds on the 2-rainbow domination number of graphs, Graphs Combin., 29 (2013) 1125–1133. | ||
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