The signed total Roman k-domatic number of a graph
نویسندگان
چکیده
منابع مشابه
The signed Roman k-domatic number of a graph
A signed Roman dominating function (SRDF) on a graph G is a function f : V (G) → {−1, 1, 2} such that u∈N [v] f(u) ≥ 1 for every v ∈ V (G), and every vertex u ∈ V (G) for which f(u) = −1 is adjacent to at least one vertex w for which f(w) = 2. A set {f1, f2, . . . , fd} of distinct signed Roman dominating functions on G with the property that ∑d i=1 fi(v) ≤ 1 for each v ∈ V (G), is called a sig...
متن کاملSigned total (k, k)-domatic number of a graph
Let G be a finite and simple graph with vertex set V (G), and let f : V (G) → {−1, 1} be a two-valued function. If k ≥ 1 is an integer and ∑x∈N(v) f(x) ≥ k for each v ∈ V (G), where N(v) is the neighborhood of v, then f is a signed total k-dominating function on G. A set {f1, f2, . . . , fd} of signed total k-dominating functions on G with the property that ∑d i=1 fi(x) ≤ k for each x ∈ V (G), ...
متن کاملThe signed Roman k-domatic number of digraphs
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...
متن کاملSIGNED STAR (k, k)-DOMATIC NUMBER OF A GRAPH
Let G be a simple graph without isolated vertices with vertex set V (G) and edge set E(G) and let k be a positive integer. A function f : E(G) −→ {−1, 1} is said to be a signed star k-dominating function on G if ∑ e∈E(v) f(e) ≥ k for every vertex v of G, where E(v) = {uv ∈ E(G) | u ∈ N(v)}. A set {f1, f2, . . . , fd} of signed star k-dominating functions on G with the property that ∑d i=1 fi(e)...
متن کاملSigned (k, k)-domatic number of a graph
Let G be a finite and simple graph with vertex set V (G), and let f: V (G)→ {−1, 1} be a two-valued function. If k > 1 is an integer and ∑ x∈N[v] f(x) > k for each v ∈ V (G), where N [v] is the closed neighborhood of v, then f is a signed k-dominating function on G. A set {f1, f2, . . . , fd} of signed kdominating functions on G with the property that ∑ d i=1 fi(x) 6 k for each x ∈ V (G), is ca...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2017
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1970