%0 Journal Article
%T Twin signed total Roman domatic numbers in digraphs
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Amjadi, Jafar
%D 2021
%\ 06/01/2021
%V 6
%N 1
%P 17-26
%! Twin signed total Roman domatic numbers in digraphs
%K twin signed total Roman dominating function
%K twin signed total Roman domination number
%K twin signed total Roman domatic number
%K Directed graph
%R 10.22049/cco.2020.26791.1142
%X 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) $sum_{xin N^-(v)}f(x)ge 1$ and $sum_{xin N^+(v)}f(x)ge 1$ for each $vin V(D)$, 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 $vin V(D)$, 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.
%U http://comb-opt.azaruniv.ac.ir/article_14024_cb9f88cbfb5b432cda02cb7e1cf7e573.pdf