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Weak signed Roman domination in graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 3، دوره 5، شماره 2، اسفند 2020، صفحه 111-123 اصل مقاله (421.3 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2019.26598.1123 | ||
| نویسنده | ||
| Lutz Volkmann* | ||
| RWTH Aachen University | ||
| چکیده | ||
| A weak signed Roman dominating function (WSRDF) of a graph $G$ with vertex set $V(G)$ is defined as a function $f:V(G)\rightarrow\{-1,1,2\}$ 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 WSRDF is the sum of its function values over all vertices. The weak signed Roman domination number of $G$, denoted by $\gamma_{wsR}(G)$, is the minimum weight of a WSRDF in $G$. We initiate the study of the weak signed Roman domination number, and we present different sharp bounds on $\gamma_{wsR}(G)$. In addition, we determine the weak signed Roman domination number of some classes of graphs. | ||
| کلیدواژهها | ||
| Domination؛ signed Roman domination؛ weak signed Roman domination | ||
| مراجع | ||
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[2] J. Amjadi, S. Nazari-Moghaddam, S.M. Sheikholeslami, and L. Volkmann, On the signed Roman k-domination in graphs, Quaest. Math. (to appear).
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[4] N. Dehgardi and L. Volkmann, Nonnegative signed Roman domination in graphs, J. Combin. Math. Combin. Comput. (to appear).
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[11] L. Volkmann, Signed total Roman k-domination in graphs, J. Combin. Math. Combin. Comput. 105 (2018), 105–116.
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