آمار
| تعداد نشریات | 7 |
| تعداد شماره‌ها | 102 |
| تعداد مقالات | 1,142 |
| تعداد مشاهده مقاله | 1,049,264 |
| تعداد دریافت فایل اصل مقاله | 868,694 |
Bounds on the restrained Roman domination number of a graph | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 6، دوره 1، شماره 1، شهریور 2016، صفحه 75-82 اصل مقاله (392.3 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2016.13556 | ||
| نویسندگان | ||
| H. Abdollahzadeh Ahangar* 1؛ S.R. Mirmehdipour2 | ||
| 1Babol Noshirvani University of Technology | ||
| 2Babol Noshirvani University of Technology | ||
| چکیده | ||
| A {\em Roman dominating function} on a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) =2$. A {\em restrained Roman dominating} function $f$ is a Roman dominating function if the vertices with label 0 induce a subgraph with no isolated vertex. The weight of a restrained Roman dominating function is the value $\omega(f)=\sum_{u\in V(G)} f(u)$. The minimum weight of a restrained Roman dominating function of $G$ is called the { \em restrained Roman domination number} of $G$ and denoted by $\gamma_{rR}(G)$. In this paper we establish some sharp bounds for this parameter. | ||
| کلیدواژه‌ها | ||
| Roman dominating function؛ Roman domination number؛ restrained Roman dominating function؛ restrained Roman domination number | ||
| مراجع | ||
|
[1] 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, 61–69.
[2] G.S. Domke, J.H. Hattingh, M.A. Henning, and L.R. Markus, Restrained domination in graphs with minimum degree two, J. Combin. Math. Combin. Comput. 35 (2000), 239–254.
[3] , Restrained domination in trees, Discrete Math. 211 (2000), no. 1, 1–9.
[4] J.H. Hattingh and E.J. Joubert, An upper bound for the restrained domination number of a graph with minimum degree at least two in terms of order and minimum degree, Discrete Appl. Math. 157 (2009), no. 13, 2846–2858.
[5] , The product of the restrained domination numbers of a graph and its complement, Acta Math. Sinica, English Series 30 (2014), no. 3, 445–452.
[6] N. Jafari Rad and M. Krzywkowski, On the restrained Roman domination in graphs, Manuscript.
[7] R.L. Pushpam and S. Padmapriea, Restrained Roman domination in graphs, Transactions on Combinatorics 4 (2015), no. 1, 1–17.
[8] C.S. ReVelle and K.E. Rosing, Defendens imperium Romanum: a classical problem in military strategy, Amer. Math. Monthly 107 (2000), no. 7, 585–594.
[9] I. Stewart, Defend the Roman empire!, Sci. Amer. 281 (1999), 136–138.
[10] D.B. West, Introduction to graph theory, vol. 2, Prentice hall Upper Saddle River, 2001. | ||
|
آمار تعداد مشاهده مقاله: 1,481 تعداد دریافت فایل اصل مقاله: 1,771 |
||