منابع مشابه
Weak signed Roman k-domination in graphs
Let $kge 1$ be an integer, and let $G$ be a finite and simple graph with vertex set $V(G)$.A weak signed Roman $k$-dominating function (WSRkDF) 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 eachvertex $vin V(G)$, where $N[v]$ is the closed neighborhood of $v$. The weight of a WSRkDF $f$ is$w(f)=sum_{vin V(G)}f(v)$. The weak si...
متن کاملRoman k-Tuple Domination in Graphs
For any integer $kgeq 1$ and any graph $G=(V,E)$ with minimum degree at least $k-1$, we define a function $f:Vrightarrow {0,1,2}$ as a Roman $k$-tuple dominating function on $G$ if for any vertex $v$ with $f(v)=0$ there exist at least $k$ and for any vertex $v$ with $f(v)neq 0$ at least $k-1$ vertices in its neighborhood with $f(w)=2$. The minimum weight of a Roman $k$-tuple dominatin...
متن کاملOn the signed Roman edge k-domination in graphs
Let $kgeq 1$ be an integer, and $G=(V,E)$ be a finite and simplegraph. The closed neighborhood $N_G[e]$ of an edge $e$ in a graph$G$ is the set consisting of $e$ and all edges having a commonend-vertex with $e$. A signed Roman edge $k$-dominating function(SREkDF) on a graph $G$ is a function $f:E rightarrow{-1,1,2}$ satisfying the conditions that (i) for every edge $e$of $G$, $sum _{xin N[e]} f...
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 کاملA note on [k, l]-sparse graphs
In this note we provide a Henneberg-type constructive characterization theorem of [k, l]-sparse graphs, that is, the graphs for which the number of induced edges in any subset X of nodes is at most k|X| − l. We consider the case 0 ≤ l ≤ k.
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ژورنال
عنوان ژورنال: Opuscula Mathematica
سال: 2013
ISSN: 1232-9274
DOI: 10.7494/opmath.2013.33.4.641