@article {
author = {Dehgardi, Nasrin and Volkmann, Lutz},
title = {Signed total Roman k-domination in directed graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {1},
number = {2},
pages = {165-178},
year = {2016},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2016.13576},
abstract = {Let $D$ be a finite and simple digraph with vertex set $V(D)$. A signed total Roman $k$-dominating function (STR$k$DF) on $D$ is a function $f:V(D)\rightarrow\{-1, 1, 2\}$ satisfying the conditions that (i) $\sum_{x\in N^{-}(v)}f(x)\ge k$ for each $v\in V(D)$, where $N^{-}(v)$ consists of all vertices of $D$ from which arcs go into $v$, and (ii) every vertex $u$ for which $f(u)=-1$ has an inner neighbor $v$ for which $f(v)=2$. The weight of an STR$k$DF $f$ is $\omega(f)=\sum_{v\in V (D)}f(v)$. The signed total Roman $k$-domination number $\gamma^{k}_{stR}(D)$ of $D$ is the minimum weight of an STR$k$DF on $D$. In this paper we initiate the study of the signed total Roman $k$-domination number of digraphs, and we present different bounds on $\gamma^{k}_{stR}(D)$. In addition, we determine the signed total Roman $k$-domination number of some classes of digraphs. Some of our results are extensions of known properties of the signed total Roman $k$-domination number $\gamma^{k}_{stR}(G)$ of graphs $G$.},
keywords = {Digraph,Signed total Roman k-dominating function,Signed total Roman k-domination},
url = {http://comb-opt.azaruniv.ac.ir/article_13576.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13576_afdcd0fac389c7cc1b729f716dbbce32.pdf}
}