Twin signed Roman domatic numbers in digraphs
نویسندگان
چکیده
منابع مشابه
Twin signed total Roman domatic numbers in digraphs
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 (...
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Let D be a finite and simple digraph with vertex set V (D), and let f : V (D) → {−1, 1} be a two-valued function. If k ≥ 1 is an integer and ∑ x∈N−[v] f(x) ≥ k for each v ∈ V (D), where N−[v] consists of v and all vertices of D from which arcs go into v, then f is a signed k-dominating function on D. A set {f1, f2, . . . , fd} of distinct signed k-dominating functions of D with the property tha...
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Let D be a finite and simple digraph with the vertex set V (D), and let f : V (D) → {−1, 1} be a two-valued function. If∑ x∈N[v] f(x) ≥ 1 for each v ∈ V (D), where N[v] consists of v and all vertices of D from which arcs go into v, then f is a signed dominating function on D. The sum f(V (D)) is called the weight w(f) of f . The minimum of weights w(f), taken over all signed dominating function...
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Let k ≥ 1 be an integer. A signed Roman k-dominating function on a digraph D is a function f : V (D) −→ {−1, 1, 2} such that ∑x∈N−[v] f(x) ≥ k for every v ∈ V (D), where N−[v] consists of v and all in-neighbors of v, and every vertex u ∈ V (D) for which f(u) = −1 has an in-neighbor w for which f(w) = 2. A set {f1, f2, . . . , fd} of distinct signed Roman k-dominating functions on D with the pro...
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Let D be a finite and simple digraph with vertex set V (D) and arc set A(D). A signed Roman dominating function (SRDF) on the digraph D is a function f : V (D) → {−1, 1, 2} satisfying the conditions that (i) ∑ x∈N−[v] f(x) ≥ 1 for each v ∈ V (D), where N −[v] consists of v and all inner neighbors of v, and (ii) every vertex u for which f(u) = −1 has an inner neighbor v for which f(v) = 2. The w...
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ژورنال
عنوان ژورنال: Tamkang Journal of Mathematics
سال: 2017
ISSN: 2073-9826,0049-2930
DOI: 10.5556/j.tkjm.48.2017.2306