نتایج جستجو برای: double roman domatic number

تعداد نتایج: 1396583  

Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:Vrightarrow{0,1,2,3}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one vertex assigned $3$ under $f$, whereas if $f(v)=1$, then the vertex $v$ must be adjacent to at least one vertex assigned $2$ or $3$. The weight of a DR...

2005
Fedor V. Fomin Fabrizio Grandoni Artem V. Pyatkin Alexey A. Stepanov

We show that the number of minimal dominating sets in a graph on n vertices is at most 1.7697, thus improving on the trivial O(2n/√n) bound. Our result makes use of the measure and conquer technique from exact algorithms, and can be easily turned into an O(1.7697) listing algorithm. Based on this result, we derive an O(2.8805n) algorithm for the domatic number problem, and an O(1.5780) algorith...

Journal: :Bulletin of The Iranian Mathematical Society 2021

A double Roman dominating function of a graph $G$ is $f:V(G)\rightarrow \{0,1,2,3\}$ having the property that for each vertex $v$ with $f(v)=0$, there exists $u\in N(v)$ $f(u)=3$, or are $u,w\in $f(u)=f(w)=2$, and if $f(v)=1$, then adjacent to assigned at least $2$ under $f$. The domination number $\gamma_{dR}(G)$ minimum weight $f(V(G))=\sum_{v\in V(G)}f(v)$ among all functions $G$. An outer i...

2017
VLADIMIR SAMODIVKIN Peter Csikvari

Let δ(G), ∆(G) and γ(G) be the minimum degree, maximum degree and domination number of a graph G = (V (G), E(G)), respectively. A partition of V (G), all of whose classes are dominating sets in G, is called a domatic partition of G. The maximum number of classes of a domatic partition of G is called the domatic number of G, denoted d(G). It is well known that d(G) ≤ δ(G)+1, d(G)γ(G) ≤ |V (G)| [...

Journal: :Australasian J. Combinatorics 2012
S. Arumugam K. Raja Chandrasekar

The domatic number d(G) of a graph G = (V,E) is the maximum order of a partition of V into dominating sets. Such a partition Π = {D1, D2, . . . , Dd} is called a minimal dominating d-partition if Π contains the maximum number of minimal dominating sets, where the maximum is taken over all d-partitions of G. The minimal dominating d-partition number Λ(G) is the number of minimal dominating sets ...

Journal: :Contributions to Discrete Mathematics 2010
Seyed Mahmoud Sheikholeslami Lutz Volkmann

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) ...

Journal: :Discrete Applied Mathematics 2010

Journal: :Mathematica Bohemica 1991

Journal: :Journal of Mathematics 2023

Domination is a well-known graph theoretic concept due to its significant real-world applications in several domains, such as design and communication network analysis, coding theory, optimization. For connected ? = V , E ...

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