TY - JOUR
AU - Mahmoodi, Akram
AU - Atapour, Maryam
AU - Norouzian, Sepideh
PY - 2022/07/29
Y2 - 2023/09/29
TI - On the signed strong total Roman domination number of graphs
JF - Tamkang Journal of Mathematics
JA - Tamkang J. Math.
VL - 54
IS - 3
SE - Papers
DO - 10.5556/j.tkjm.54.2023.3907
UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3907
SP - 265-280
AB - <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>
ER -