Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21286220211201Signed total Italian k-domination in graphs1711831411210.22049/cco.2020.26919.1164ENLutzVolkmannRWTH Aachen University0000-0003-3496-277XJournal Article20200819Let $kge 1$ be an integer, and let $G$ be a finite and simple graph with vertex set $V(G)$. A signed total Italian $k$-ominating function (STIkDF) on a graph $G$ is a function $f:V(G)rightarrow{-1,1,2}$ satisfying the conditions that $sum_{xin N(v)}f(x)ge k$ for each vertex $vin V(G)$, where $N(v)$ is the neighborhood of $v$, and each vertex $u$ with $f(u)=-1$ is adjacent to a vertex $v$ with $f(v)=2$ or to two vertices $w$ and $z$ with $f(w)=f(z)=1$. The weight of an STIkDF $f$ is $omega(f)=sum_{vin V(G)}f(v)$. The signed total Italian $k$-domination number $gamma_{stI}^k(G)$ of $G$ is the minimum weight of an STIkDF on $G$. In this paper we initiate the study of the signed total Italian $k$-domination number of graphs, and we present different bounds on $gamma_{stI}^k(G)$. In addition, we determine the<br />signed total Italian $k$-domination number of some classes of graphs. Some of our results are extensions of well-known properties of the signed total Roman $k$-domination number $gamma_{stR}^k(G)$, introduced and investigated by Volkmann [9,12].http://comb-opt.azaruniv.ac.ir/article_14112_c58a0b3d2443dd19b119a3177bde3a4c.pdf