let $d=(v,a)$ be a finite simple directed graph. a function$f:vlongrightarrow {-1,0,1}$ is called a twin minus dominatingfunction (tmdf) if $f(n^-[v])ge 1$ and $f(n^+[v])ge 1$ for eachvertex $vin v$. the twin minus domination number of $d$ is$gamma_{-}^*(d)=min{w(f)mid f mbox{ is a tmdf of } d}$. inthis paper, we initiate the study of twin minus domination numbersin digraphs and present some lo...

Let $D=(V,A)$ be a finite simple directed graph. A function$f:Vlongrightarrow {-1,0,1}$ is called a twin minus dominatingfunction (TMDF) if $f(N^-[v])ge 1$ and $f(N^+[v])ge 1$ for eachvertex $vin V$. The twin minus domination number of $D$ is$gamma_{-}^*(D)=min{w(f)mid f mbox{ is a TMDF of } D}$. Inthis paper, we initiate the study of twin minus domination numbersin digraphs and present some lo...

In many papers, the relation between the domination number of a product of graphs and the product of domination numbers of factors is studied. Here we investigate this problem for domination and total domination numbers in the cross product of digraphs. We give analogues of known results for graphs, and we also present new results for digraphs with sources. Using these results we find dominatio...

Zero forcing is a propagation process on a graph, or digraph, defined in linear algebra to provide a bound for the minimum rank problem. Independently, zero forcing was introduced in physics, computer science and network science, areas where line digraphs are frequently used as models. Zero forcing is also related to power domination, a propagation process that models the monitoring of electric...

The reinforcement number of a graph G is the minimum cardinality of a set of extra edges whose addition results in a graph with domination number less than the domination number of G. In this paper we consider this parameter for digraphs, investigate the relationship between reinforcement numbers of undirected graphs and digraphs, and obtain further results for regular graphs. We also determine...

Let $D$ be a finite simple digraph with vertex set $V(D)$ and arcset $A(D)$. A twin signed total Roman dominating function (TSTRDF) on thedigraph $D$ is a function $f:V(D)rightarrow{-1,1,2}$ satisfyingthe 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 (...