منابع مشابه
The Italian domatic number of a digraph
An {em Italian dominating function} on a digraph $D$ with vertex set $V(D)$ is defined as a function$fcolon V(D)to {0, 1, 2}$ such that every vertex $vin V(D)$ with $f(v)=0$ has at least two in-neighborsassigned 1 under $f$ or one in-neighbor $w$ with $f(w)=2$. A set ${f_1,f_2,ldots,f_d}$ of distinctItalian dominating functions on $D$ with the property that $sum_{i=1}^d f_i(v)le 2$ for each $vi...
متن کاملA note on the Roman domatic number of a digraph
Roman dominating function} on a digraph $D$ with vertex set $V(D)$ is a labeling$fcolon V(D)to {0, 1, 2}$such that every vertex with label $0$ has an in-neighbor with label $2$. A set ${f_1,f_2,ldots,f_d}$ ofRoman dominating functions on $D$ with the property that $sum_{i=1}^d f_i(v)le 2$ for each $vin V(D)$,is called a {em Roman dominating family} (of functions) on $D$....
متن کاملThe Roman Domination Number of a Digraph
LetD = (V,A) be a finite and simple digraph. A Roman dominating function (RDF) on a digraph D is a labeling f : V (D) → {0, 1, 2} such that every vertex with label 0 has a in-neighbor with label 2. The weight of an RDF f is the value ω(f) = ∑ v∈V f(v). The Roman domination number of a digraph D, denoted by γR(D), equals the minimum weight of an RDF on D. In this paper we present some sharp boun...
متن کاملThe circular chromatic number of a digraph
We introduce the circular chromatic number χc of a digraph and establish various basic results. They show that the coloring theory for digraphs is similar to the coloring theory for undirected graphs when independent sets of vertices are replaced by acyclic sets. Since the directed k-cycle has circular chromatic number k/(k − 1), for k ≥ 2, values of χc between 1 and 2 are possible. We show tha...
متن کاملThe Reversing Number of a Digraph
A minimum reversing set of a digraph is a smallest sized set of arcs which when reversed makes the digraph acyclic. We investigate a related issue: Given an acyclic digraph D, what is the size of a smallest tournataent T which has the arc set of D as a minimum reversing set? We show that such a T always exists and define the reversing number ofan acyclic digraph to be the number of vertices in ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1982
ISSN: 0095-8956
DOI: 10.1016/0095-8956(82)90046-6