Remarks on the minus (signed) total domination in graphs
نویسندگان
چکیده
منابع مشابه
Nonnegative signed total Roman domination in graphs
Let $G$ be a finite and simple graph with vertex set $V(G)$. A nonnegative signed total Roman dominating function (NNSTRDF) on a graph $G$ is a function $f:V(G)rightarrow{-1, 1, 2}$ satisfying the conditionsthat (i) $sum_{xin N(v)}f(x)ge 0$ for each $vin V(G)$, where $N(v)$ is the open neighborhood of $v$, and (ii) every vertex $u$ for which $f(u...
متن کاملSigned total Italian k-domination in graphs
Let k ≥ 1 be an integer, and let G be a finite and simple graph with vertex set V (G). A signed total Italian k-dominating function (STIkDF) on a graph G is a functionf : V (G) → {−1, 1, 2} satisfying the conditions that $sum_{xin N(v)}f(x)ge k$ for each vertex v ∈ 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 vertic...
متن کاملThe minus k-domination numbers in graphs
For any integer , a minus k-dominating function is afunction f : V (G) {-1,0, 1} satisfying w) for every vertex v, where N(v) ={u V(G) | uv E(G)} and N[v] =N(v)cup {v}. The minimum of the values of v), taken over all minusk-dominating functions f, is called the minus k-dominationnumber and is denoted by $gamma_k^-(G)$ . In this paper, we introduce the study of minu...
متن کاملA note on signed and minus domination in graphs
In this paper, we give upper bounds on the upper signed domination number of [l, k] graphs, which generalize some results obtained in other papers. Further, good lower bounds are established for the minus ksubdomination number γ−101 ks and signed k-subdomination number γ −11 ks .
متن کاملSigned total Roman k-domination in directed graphs
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 conditionsthat (i) $sum_{xin N^{-}(v)}f(x)ge k$ for each$vin V(D)$, where $N^{-}(v)$ consists of all vertices of $D$ fromwhich arcs go into $v$, and (ii) every vertex $u$ for which$f(u)=-1$ has a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.06.015