نتایج جستجو برای Roman domination

تعداد نتایج: 8047

## Roman Domination

2015
LINFENG XU,

In his article published in 1999, Ian Stewart discussed a strategy of Emperor Constantine for defending the Roman Empire. Motivated by this article, Cockayne et al.(2004) introduced the notion of Roman domination in graphs. Let G = (V,E) be a graph. A Roman dominating function of G is a function f : V → {0, 1, 2} such that every vertex v for which f(v) = 0 has a neighbor u with f(u) = 2. The we...

## Thresholds for Roman domination

2006
Noah Prince,

Define a Roman dominating function (RDF) of a graph G to be a function f : V (G) → {0, 1, 2} such that every u with f(u) = 0 has a neighbor v with f(v) = 2. The weight of f , w(f), is ∑ v∈V (G) f(v). The Roman domination number of G, γR(G), is the minimum weight of an RDF of G. It is easy to see that γ(G) ≤ γR(G) ≤ 2γ(G), where γ(G) is the domination number of G. In this paper, we determine pro...

## Roman domination perfect graphs

2012
Nader Jafari Rad, Lutz Volkmann,

A Roman dominating function on a graphG is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u ∈ V (G) for which f(u) = 0 is adjacent to at least one vertex v ∈ V (G) for which f(v) = 2. The weight of a Roman dominating function is the value f(V (G)) = ∑ u∈V (G) f(u). The Roman domination number γR(G) of G is the minimum weight of a Roman dominating function on G. A Ro...

## Roman Domination on Graphs

2009
Gerard Jennhwa Chang,

Recent articles by ReVelle [20, 21] in the Johns Hopkins Magazines suggested a new variation of domination called Roman domination, see also [22] for an integer programming formulation of the problem. Since then, there have been several articles on Roman domination and its variations [2, 3, 4, 5, 6, 11, 12, 14, 15, 16, 18, 24, 23, 25]. Emperor Constantine had the requirement that an army or leg...

## Fractional Roman Domination

2007
Robert R. Rubalcaba, Matt Walsh,

A function f : V (G) → {0, 1, 2} is a Roman dominating function if for every vertex with f(v) = 0, there exists a vertex w ∈ N(v) with f(w) = 2. We introduce two fractional Roman domination parameters, γR ◦ f and γRf , from relaxations of two equivalent integer programming formulations of Roman domination (the former using open neighborhoods and the later using closed neighborhoods in the Roman...

## Roman domination in graphs

Journal: :Discrete Mathematics 2004
Ernest J. Cockayne, Paul A. Dreyer, Sandra Mitchell Hedetniemi, Stephen T. Hedetniemi,

A Roman dominating function on a graph G = (V, E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V ) = ∑ u∈V f(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G. In this pape...

## Roman domination excellent graphs: trees

2018

A Roman dominating function (RDF) on a graph \$G = (V, E)\$ is a labeling \$f : V rightarrow {0, 1, 2}\$ suchthat every vertex with label \$0\$ has a neighbor with label \$2\$. The weight of \$f\$ is the value \$f(V) = Sigma_{vin V} f(v)\$The Roman domination number, \$gamma_R(G)\$, of \$G\$ is theminimum weight of an RDF on \$G\$.An RDF of minimum weight is called a \$gamma_R\$-function.A graph G is said to be \$g...

## Co-Roman domination in trees

2020

Abstract: Let G=(V,E) be a graph and let f:V(G)→{0,1,2} be a function‎. ‎A vertex v is protected with respect to f‎, ‎if f(v)>0 or f(v)=0 and v is adjacent to a vertex of positive weight‎. ‎The function f is a co-Roman dominating function‎, ‎abbreviated CRDF if‎: ‎(i) every vertex in V is protected‎, ‎and (ii) each u∈V with positive weight has a neighbor v∈V with f(v)=0 such that the func...

## On trees with equal Roman domination and outer-independent Roman domination numbers

2019

A Roman dominating function (RDF) on a graph \$G\$ is a function \$f : V (G) to {0, 1, 2}\$satisfying the condition that every vertex \$u\$ for which \$f(u) = 0\$ is adjacent to at least onevertex \$v\$ for which \$f(v) = 2\$. A Roman dominating function \$f\$ is called an outer-independentRoman dominating function (OIRDF) on \$G\$ if the set \${vin Vmid f(v)=0}\$ is independent.The (outer-independent) Roman dom...

## A characterization of trees with equal Roman 2-domination and Roman domination numbers

2019

Given a graph \$G=(V,E)\$ and a vertex \$v in V\$, by \$N(v)\$ we represent the open neighbourhood of \$v\$. Let \$f:Vrightarrow {0,1,2}\$ be a function on \$G\$. The weight of \$f\$ is \$omega(f)=sum_{vin V}f(v)\$ and let \$V_i={vin V colon f(v)=i}\$, for \$i=0,1,2\$. The function \$f\$ is said to bebegin{itemize}item a Roman \${2}\$-dominating function, if for every vertex \$vin V_0\$, \$sum_{uin N(v)}f(u)geq 2\$. The R...

نمودار تعداد نتایج جستجو در هر سال

با کلیک روی نمودار نتایج را به سال انتشار فیلتر کنید