نتایج جستجو برای outer-independent double Italian domination

تعداد نتایج: 554374

## Bounds on the outer-independent double Italian domination number

2021

An outer-independent double Italian dominating function (OIDIDF)on a graph \$G\$ with vertex set \$V(G)\$ is a function\$f:V(G)longrightarrow {0,1,2,3}\$ such that if \$f(v)in{0,1}\$ for a vertex \$vin V(G)\$ then \$sum_{uin N[v]}f(u)geq3\$,and the set \$ {uin V(G)|f(u)=0}\$ is independent. The weight ofan OIDIDF \$f\$ is the value \$w(f)=sum_{vin V(G)}f(v)\$. Theminimum weight of an OIDIDF on a graph \$G\$ is cal...

## Outer independent Roman domination number of trees

2021

‎A Roman dominating function (RDF) on a graph G=(V,E) is a function  f : V → {0, 1, 2}  such that every vertex u for which f(u)=0 is‎ ‎adjacent to at least one vertex v for which f(v)=2‎. ‎An RDF f is called‎‎an outer independent Roman dominating function (OIRDF) if the set of‎‎vertices assigned a 0 under f is an independent set‎. ‎The weight of an‎‎OIRDF is the sum of its function values over ...

## 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...

## On trees with double domination number equal to 2-outer-independent domination number plus one

2011
Marcin Krzywkowski,

A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. For a graph G = (V,E), a subset D ⊆ V (G) is a 2dominating set if every vertex of V (...

## Total outer-independent domination in graphs

2014
Marcin Krzywkowski,

We initiate the study of total outer-independent domination in graphs. A total outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V (G) \ D is independent. The total outer-independent domination number of a graph G is the minimum cardinality of a total outer-independent dominating set of G. First we discuss the ...

## On the outer independent 2-rainbow domination number of Cartesian products of paths and cycles

2021

‎Let G be a graph‎. ‎A 2-rainbow dominating function (or‎ 2-RDF) of G is a function f from V(G)‎ ‎to the set of all subsets of the set {1,2}‎ ‎such that for a vertex v ∈ V (G) with f(v) = ∅, ‎the‎‎condition \$bigcup_{uin N_{G}(v)}f(u)={1,2}\$ is fulfilled‎, wher NG(v)  is the open neighborhood‎‎of v‎. ‎The weight of 2-RDF f of G is the value‎‎\$omega (f):=sum _{vin V(G)}|f(v)|\$‎. ‎The 2-rainbow‎‎d...

## A Lower Bound on the Double Outer-independent Domination Number of a Tree

2012
Marcin Krzywkowski, M. Krzywkowski,

A vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D, and the set V (G) \D is independent. The double outer-independent domination number of a graph G, denoted by γ d (G), is the minimum cardinality of a double outer-indepe...

## Signed total Italian k-domination in graphs

2021

Let k ≥ 1 be an integer, and let G be a finite and simple graph with vertex set V (G). A signed total Italian k-dominating function (STIkDF) on a graph G is a functionf : V (G) → {−1, 1, 2} satisfying the conditions that \$sum_{xin N(v)}f(x)ge k\$ for each vertex v ∈ V (G), where N(v) is the neighborhood of \$v\$, and each vertex u with f(u)=-1 is adjacent to a vertex v with f(v)=2 or to two vertic...

## Independent domination in directed graphs

2021

In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...

## On Trees with Equal Total Domination and 2-outer-independent Domination Numbers

2014
MARCIN KRZYWKOWSKI, Ioan Tomescu, Marcin Krzywkowski,

For a graph G = (V,E), a subset D ⊆ V (G) is a total dominating set if every vertex of G has a neighbor in D. The total domination number of G is the minimum cardinality of a total dominating set of G. A subset D ⊆ V (G) is a 2-dominating set of G if every vertex of V (G) \ D has at least two neighbors in D, while it is a 2-outer-independent dominating set of G if additionally the set V (G) \ D...

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