@article{Mahmoodi_Atapour_Norouzian_2022, title={ On the signed strong total Roman domination number of graphs}, volume={54}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3907}, DOI={10.5556/j.tkjm.54.2023.3907}, abstractNote={<p>Let $G=(V,E)$ be a finite and simple graph of order $n$ and maximum<br>degree $\Delta$. A signed strong total Roman dominating function on<br>a graph $G$ is a function $f:V(G)\rightarrow\{-1, 1,2,\ldots, \lceil<br>\frac{\Delta}{2}\rceil+1\}$ satisfying the condition that (i) for<br>every vertex $v$ of $G$, $f(N(v))=\sum_{u\in N(v)}f(u)\geq 1$, where<br>$N(v)$ is the open neighborhood of $v$ and (ii) every vertex $v$ for<br>which $f(v)=-1$ is adjacent to at least one vertex<br>$w$ for which $f(w)\geq 1+\lceil\frac{1}{2}\vert N(w)\cap V_{-1}\vert\rceil$, where<br>$V_{-1}=\{v\in V: f(v)=-1\}$.<br>The minimum of the<br>values $\omega(f)=\sum_{v\in V}f(v)$, taken over all signed strong<br>total Roman dominating functions $f$ of $G$, is called the signed strong total<br>Roman domination number of $G$ and is denoted by $\gamma_{ssTR}(G)$.<br>In this paper, we initiate signed strong total Roman domination number of a graph and give<br>several bounds for this parameter. Then, among other results, we determine the signed strong total Roman domination<br>number of special classes of graphs.</p>}, number={3}, journal={Tamkang Journal of Mathematics}, author={Mahmoodi, Akram and Atapour, Maryam and Norouzian, Sepideh}, year={2022}, month={Jul.}, pages={265–280} }