منابع مشابه
Weak signed Roman domination in graphs
A {em weak signed Roman dominating function} (WSRDF) of a graph $G$ with vertex set $V(G)$ is defined as afunction $f:V(G)rightarrow{-1,1,2}$ having the property that $sum_{xin N[v]}f(x)ge 1$ for each $vin V(G)$, where $N[v]$ is theclosed neighborhood of $v$. The weight of a WSRDF is the sum of its function values over all vertices.The weak signed Roman domination number of $G...
متن کاملWeak 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 کاملWeak Roman domination in graphs
Let G = (V,E) be a graph and f be a function f : V → {0, 1, 2}. A vertex u with f(u) = 0 is said to be undefended with respect to f , if it is not adjacent to a vertex with positive weight. The function f is a weak Roman dominating function (WRDF) if each vertex u with f(u) = 0 is adjacent to a vertex v with f(v) > 0 such that the function f ′ : V → {0, 1, 2} defined by f ′ (u) = 1, f ′ (v) = f...
متن کاملWeak edge Roman domination in graphs
Let G = (V,E) be a graph and let f be a function f : E → {0, 1, 2}. An edge x with f(x) = 0 is said to be undefended with respect to f if it is not incident to an edge with positive weight. The function f is a weak edge Roman dominating function (WERDF) if each edge x with f(x) = 0 is incident to an edge y with f(y) > 0 such that the function f ′ : E → {0, 1, 2}, defined by f ′(x) = 1, f ′(y) =...
متن کاملNonnegative 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...
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ژورنال
عنوان ژورنال: Malaya Journal of Matematik
سال: 2021
ISSN: 2319-3786,2321-5666
DOI: 10.26637/mjm0901/0082