منابع مشابه
Induced-paired Domatic Numbers of Graphs
A subset D of the vertex set V (G) of a graph G is called dominating in G, if each vertex of G either is in D, or is adjacent to a vertex of D. If moreover the subgraph 〈D〉 of G induced by D is regular of degree 1, then D is called an induced-paired dominating set in G. A partition of V (G), each of whose classes is an induced-paired dominating set in G, is called an induced-paired domatic part...
متن کاملPoint-set Domatic Numbers of Graphs
A subset D of the vertex set V (G) of a graph G is called point-set dominating, if for each subset S ⊆ V (G) − D there exists a vertex v ∈ D such that the subgraph of G induced by S ∪ {v} is connected. The maximum number of classes of a partition of V (G), all of whose classes are point-set dominating sets, is the point-set domatic number dp(G) of G. Its basic properties are studied in the paper.
متن کاملDouble Roman domination and domatic numbers of graphs
A double Roman dominating function on a graph $G$ with vertex set $V(G)$ is defined in cite{bhh} as a function$f:V(G)rightarrow{0,1,2,3}$ having the property that if $f(v)=0$, then the vertex $v$ must have at least twoneighbors assigned 2 under $f$ or one neighbor $w$ with $f(w)=3$, and if $f(v)=1$, then the vertex $v$ must haveat least one neighbor $u$ with $f(u)ge 2$. The weight of a double R...
متن کاملSigned k-domatic numbers of graphs
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 that ∑...
متن کاملOn the signed total domatic numbers of directed graphs
Let D = (V,A) be a finite simple directed graph (shortly digraph) in which dD(v) ≥ 1 for all v ∈ V . A function f : V −→ {−1, 1} is called a signed total dominating function if ∑ u∈N−(v) f(u) ≥ 1 for each vertex v ∈ V . A set {f1, f2, . . . , fd} of signed total dominating functions on D with the property that ∑d i=1 fi(v) ≤ 1 for each v ∈ V (D), is called a signed total dominating family (of f...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky
سال: 1981
ISSN: 0528-2195
DOI: 10.21136/cpm.1981.108482