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Weak signed double Roman domination in graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 03 دی 1403 اصل مقاله (431.49 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 | ||
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