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Twin signed total Roman domatic numbers in digraphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 2، دوره 6، شماره 1، شهریور 2021، صفحه 17-26 اصل مقاله (368.66 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2020.26791.1142 | ||
| نویسنده | ||
| Jafar Amjadi* | ||
| Azarbaijan | ||
| چکیده | ||
| Let $D$ be a finite simple digraph with vertex set $V(D)$ and arc set $A(D)$. A twin signed total Roman dominating function (TSTRDF) on the digraph $D$ is a function $f:V(D)\rightarrow\{-1,1,2\}$ satisfying the conditions that (i) $\sum_{x\in N^-(v)}f(x)\ge 1$ and $\sum_{x\in N^+(v)}f(x)\ge 1$ for each $v\in V(D)$, where $N^-(v)$ (resp. $N^+(v)$) consists of all in-neighbors (resp. out-neighbors) of $v$, and (ii) every vertex $u$ for which $f(u)=-1$ has an in-neighbor $v$ and an out-neighbor $w$ with $f(v)=f(w)=2$. A set $\{f_1,f_2,\ldots,f_d\}$ of distinct twin signed total Roman dominating functions on $D$ with the property that $\sum_{i=1}^df_i(v)\le 1$ for each $v\in V(D)$, is called a twin signed total Roman dominating family (of functions) on $D$. The maximum number of functions in a twin signed total Roman dominating family on $D$ is the twin signed total Roman domatic number of $D$, denoted by $d_{stR}^*(D)$. In this paper, we initiate the study of the twin signed total Roman domatic number in digraphs and present some sharp bounds on $d_{stR}^*(D)$. In addition, we determine the twin signed total Roman domatic number of some classes of digraphs. | ||
| کلیدواژهها | ||
| twin signed total Roman dominating function؛ twin signed total Roman domination number؛ twin signed total Roman domatic number؛ directed graph | ||
| مراجع | ||
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