论文标题
意大利的束缚和挖掘数量
The Italian bondage and reinforcement numbers of digraphs
论文作者
论文摘要
\ textIt {textit {意大利主导函数}在带有顶点套装$ v（d）$的digraph $ d $上定义为函数$ f：v（d）\ rightarrow \ {0，1，2 \} $，使每个顶点$ v \ in v（d $ f（v）n $ f（v）至少$ f $ n $ 1 $ 1 $ 1 $ 1 $ 1 $ 1 $ nneigh nneigh $ w $ with $ f（w）= 2 $。意大利主导函数$ f $的\ textit {werge}是$ω（f）= f（v（d））= \ sum_ {u \ in V（d）} f（u）$。 Digraph $ d $的\ textit {意大利统治编号}，用$γ_i（d）$表示，是$ d $上所有意大利主导函数的权重。 Digraph $ d $的\ textit {意大利债券编号}，用$ b_i（d）$表示，是$ a（d）$的最小弧数，其在$ d $中删除的ARC $ a（d）$ d $ digraph $ d $ d'$ d'$ d'$ d'$ d'$，$γ_i（d'）>γ_i（d）$γ_i（d）$。 Digraph $ d $的\ textit {italian加固号}，用$ r_i（d）$表示，是$ d $添加的额外弧的最小数量，在$γ_i（d'）<γ_i（d）$（d）$中添加了$ d $。在本文中，我们启动了意大利束缚和加强数字的研究，并为$ b_i（d）$和$ r_i（d）$提出了一些界限。我们还确定了某些类别的束缚的意大利束缚和加强数量。
An \textit{Italian dominating function} on a digraph $D$ with vertex set $V(D)$ is defined as a function $f : V(D) \rightarrow \{0, 1, 2\}$ such that every vertex $v \in V(D)$ with $f(v) = 0$ has at least two in-neighbors assigned $1$ under $f$ or one in-neighbor $w$ with $f(w) = 2$. The \textit{weight} of an Italian dominating function $f$ is the value $ω(f) = f(V(D)) = \sum_{u \in V(D)} f(u)$. The \textit{Italian domination number} of a digraph $D$, denoted by $γ_I(D)$, is the minimum taken over the weights of all Italian dominating functions on $D$. The \textit{Italian bondage number} of a digraph $D$, denoted by $b_I(D)$, is the minimum number of arcs of $A(D)$ whose removal in $D$ results in a digraph $D'$ with $γ_I(D') > γ_I(D)$. The \textit{Italian reinforcement number} of a digraph $D$, denoted by $r_I(D)$, is the minimum number of extra arcs whose addition to $D$ results in a digraph $D'$ with $γ_I(D') < γ_I(D)$. In this paper, we initiate the study of Italian bondage and reinforcement numbers in digraphs and present some bounds for $b_I(D)$ and $r_I(D)$. We also determine the Italian bondage and reinforcement numbers of some classes of digraphs.
