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Weak signed total Italian domination in digraphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 22 مهر 1404 اصل مقاله (405.85 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30748.2606 | ||
| نویسنده | ||
| Lutz Volkmann* | ||
| RWTH Aachen University, , 52056 Aachen, Germany | ||
| چکیده | ||
| A weak signed total Italian dominating function (WSTIDF) of a digraph $D$ with vertex set $V(D)$ is defined as a function $f:V(D)\rightarrow\{-1,1,2\}$ having the property that $\sum_{x\in N^-(v)}f(x)\ge 1$ for each $v\in V(D)$, where $N^-(v)$ consists of all vertices of $D$ from which arcs go into $v$. The weight of a WSTIDF is the sum of its function values over all vertices. The weak signed total Italian domination number of $D$, denoted by $\gamma_{wstI}(D)$, is the minimum weight of a WSTIDF on $D$. We initiate the study of the weak signed total Italian domination number in digraphs, and we present different sharp bounds on $\gamma_{wstI}(D)$. In addition, we determine the weak signed total Italian domination number of some classes of digraphs. | ||
| کلیدواژهها | ||
| Digraphs؛ Weak signed total Italian domination؛ signed total Italian domination؛ signed total Roman domination؛ total domination | ||
| مراجع | ||
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[1] H. Abdollahzadeh Ahangar, M.A. Henning, C. Löwenstein, Y. Zhao, andV. Samodivkin, Signed Roman domination in graphs, J. Comb. Optim. 27 (2014), no. 2, 241–255. https://doi.org/10.1007/s10878-012-9500-0
[2] 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 International Publishing, Cham, 2020, pp. 365–409. [3] M. Chellali, N. Jafari Rad, S.M. Sheikholeslami, and L. Volkmann, A survey on Roman domination parameters in directed graphs, J. Combin. Math. Combin. Comput. 115 (2020), 141–171.
[4] 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. https://doi.org/10.1016/j.akcej.2019.12.001
[5] 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 International Publishing, Cham, 2021, pp. 273–307.
[6] N. Dehgardi and L. Volkmann, Nonnegative signed Roman domination in graphs, J. Combin. Math. Combin. Comput. 110 (2019), 259–277.
[7] F. Harary, R.Z. Norman, and D. Cartwright, Structural Models: An Introduction to the Theory of Directed Graphs, vol. 82, Wiley New York, 1965.
[8] T.W. Haynes, S. Hedetniemi, and P. Slater, Fundamentals of Domination in Graphs, CRC press, 2013.
[9] 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 [10] M.A. Henning and L. Volkmann, Signed Roman $k$-domination in graphs, Graphs Combin. 32 (2016), no. 1, 175–190. https://doi.org/10.1007/s00373-015-1536-3 [11] Volkmann, On the signed total Roman domination and domatic numbers of graphs, Discrete Appl. Math. 214 (2016), 179–186. https://doi.org/10.1016/j.dam.2016.06.006
[12] L. Volkmann, Signed total Roman domination in graphs, J. Comb. Optim. 32 (2016), no. 3, 855–871. https://doi.org/10.1007/s10878-015-9906-6
[13] L. Volkmann, Signed total Roman domination in digraphs, Discuss. Math. Graph Theory 37 (2017), no. 1, 261–272.
[14] L. Volkmann, Signed total Roman k-domination in graphs, J. Combin. Math. Combin. Comput. 105 (2018), 105–116.
[15] L. Volkmann, Signed total Italien domination in graphs, J. Combin. Math. Combin. Comput. 115 (2020), 291–305.
[16] L. Volkmann, Signed total Italian domination in digraphs, Commun. Comb. Optim. 8 (2023), no. 3, 457–466. https://doi.org/10.22049/cco.2022.27700.1318 | ||
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