آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 122 |
| تعداد مقالات | 1,538 |
| تعداد مشاهده مقاله | 1,624,402 |
| تعداد دریافت فایل اصل مقاله | 1,523,816 |
Weak signed double Roman domination in graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 2، دوره 11، شماره 3، آذر 2026، صفحه 739-756 اصل مقاله (431.2 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.30016.2268 | ||
| نویسنده | ||
| Lutz Volkmann* | ||
| RWTH Aachen University, 52056 Aachen, Germany | ||
| چکیده | ||
| A weak signed double Roman dominating function (WSDRDF) of a graph $G$ with vertex set $V(G)$ is defined as a function $f:V(G)\rightarrow\{-1,1,2,3\}$ having the property that $\sum_{x\in N[v]}f(x)\ge 1$ for each $v\in V(G)$, where $N[v]$ is the closed neighborhood of $v$. The weight of a WSDRDF is the sum of its function values over all vertices. The weak signed double Roman domination number of $G$, denoted by $\gamma_{wsdR}(G)$, is the minimum weight of a WSDRDF in $G$. We initiate the study of the weak signed double Roman domination number, and we present different sharp bounds on $\gamma_{wsdR}(G)$. In addition, we determine the weak signed double Roman domination number of some classes of graphs. | ||
| کلیدواژهها | ||
| Domination؛ signed double Roman domination؛ weak signed double Roman domination | ||
| مراجع | ||
|
[1] H. Abdollahzadeh Ahangar, M. Chellali, and S.M. Sheikholeslami, Signed double Roman domination in graphs, Discrete Appl. Math. 257 (2019), 1–11. https://doi.org/10.1016/j.dam.2018.09.009
[2] H. Abdollahzadeh Ahangar, M. Chellali, and S.M. Sheikholeslami, Signed double Roman domination in graphs, Filomat 33 (2019), 121–134.
[3] H Abdollahzadeh Ahangar, M.A. Henning, C. L¨owenstein, Y. Zhao, and V. Samodivkin, Signed Roman domination in graphs, J. Comb. Optim. 27 (2014), no. 2, 241–255. https://doi.org/10.1007/s10878-012-9500-0
[4] L. Asgharsharghi, R. Khoeilar, and S.M. Sheikholeslami, Signed strong Roman domination in graphs, Tamkang J. Math. 48 (2017), no. 2, 135–147.
[5] M. Chellali, N. Jafari Rad, S.M. Sheikholeslami, and L. Volkmann, Roman Domination in Graphs, pp. 365–409, Springer International Publishing, Cham, 2020.
[6] M. Chellali, N. Jafari Rad, S.M. Sheikholeslami, and L. Volkmann, Varieties of roman domination, pp. 273–307, Springer International Publishing, Cham, 2021.
[7] 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. https://doi.org/10.1016/j.disc.2003.06.004
[8] N. Dehgardi and L. Volkmann, Nonnegative signed total Roman domination in graphs, Commun. Comb. Optim. 5 (2020), no. 2, 139–155. https://doi.org/10.22049/cco.2019.26599.1124
[9] T.W. Haynes, S. Hedetniemi, and P. Slater, Fundamentals of Domination in Graphs, CRC press, 2013.
[10] M.A. Henning and L. Volkmann, Signed Roman $k$-domination in trees, Discrete Appl. Math. 186 (2015), 98–105. https://doi.org/10.1016/j.dam.2015.01.019
[11] L. Volkmann, Weak signed Roman $k$-domatic number of a graph, Commun. Comb. Optim. 7 (2022), no. 1, 17–27. https://doi.org/10.22049/cco.2021.26998.1178 | ||
|
آمار تعداد مشاهده مقاله: 225 تعداد دریافت فایل اصل مقاله: 280 |
||