# Wyniki wyszukiwania dla: domination number - MOST Wiedzy

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Wyniki wyszukiwania dla: domination number
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### Wyniki wyszukiwania dla: domination number

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

Publikacja

- Rok 2013

A vertex of a graph is said to dominate itself and all of its neighbors. A subset D subseteq V(G) is a 2-dominating set of G if every vertex of V(G)D is dominated by at least two vertices of D, while it is a double dominating set of G if every vertex of G is dominated by at least two vertices of D. The 2-domination (double domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (double dominating,...

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• #### On trees with double domination number equal to total domination number plus one

Publikacja

- Rok 2011

A total 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. 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 total (double, respectively) domination number of a graph G is the minimum cardinality of a total (double,...

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

Publikacja

- Rok 2012

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 subseteq V(G) is a 2-dominating set if every vertex of V(G)D has at least two neighbors...

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• #### Isolation Number versus Domination Number of Trees

Publikacja
• M. Lemańska
• M. J. Souto-Salorio
• A. Dapena
• F. Vazquez-Araujo

- Rok 2021

If G=(VG,EG) is a graph of order n, we call S⊆VG an isolating set if the graph induced by VG−NG[S] contains no edges. The minimum cardinality of an isolating set of G is called the isolation number of G, and it is denoted by ι(G). It is known that ι(G)≤n3 and the bound is sharp. A subset S⊆VG is called dominating in G if NG[S]=VG. The minimum cardinality of a dominating set of G is the domination number, and it is denoted by γ(G)....

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• #### Complexity Issues on of Secondary Domination Number

Publikacja

- Rok 2023

In this paper we study the computational complexity issues of the problem of secondary domination (known also as (1, 2)-domination) in several graph classes. We also study the computational complexity of the problem of determining whether the domination and secondary domination numbers are equal. In particular, we study the influence of triangles and vertices of degree 1 on these numbers. Also, an optimal algorithm for finding...

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• #### On the total restrained domination number of a graph

Publikacja

- Rok 2006

W pracy przedstawione są ograniczenia i własności liczby dominowania podwójnie totalnego.

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• #### The outer-connected domination number of a graph

Publikacja

- Rok 2007

W pracy została zdefiniowana liczba dominowania zewnętrznie spójnego i przedstawiono jej podstawowe własności.

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• #### Lower bound on the domination number of a tree.

Publikacja

- Rok 2004

W pracy przedstawiono dolne ograniczenie na liczbę dominowania w drzewach oraz przedstawiono pełną charakterystykę grafów ekstremalnych.

• #### On the doubly connected domination number of a graph

Publikacja

- Rok 2006

W pracy została zdefiniowana liczba dominowania podwójnie spójnego i przedstawiono jej podstawowe własności.

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• #### On the super domination number of lexicographic product graphs

Publikacja

- Rok 2019

The neighbourhood of a vertexvof a graphGis the setN(v) of all verticesadjacent tovinG. ForD⊆V(G) we defineD=V(G)\D. A setD⊆V(G) is called a super dominating set if for every vertexu∈D, there existsv∈Dsuch thatN(v)∩D={u}. The super domination number ofGis theminimum cardinality among all super dominating sets inG. In this article weobtain closed formulas and tight bounds for the super dominating number oflexicographic product...

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• #### Influence of edge subdivision on the convex domination number

Publikacja

- Rok 2012

We study the influence of edge subdivision on the convex domination number. We show that in general an edge subdivision can arbitrarily increase and arbitrarily decrease the convex domination number. We also find some bounds for unicyclic graphs and we investigate graphs G for which the convex domination number changes after subdivision of any edge in G.

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Publikacja

- Rok 2014

• #### Trees with equal restrained domination and total restrained domination numbers

Publikacja

- Rok 2007

W publikacji scharakteryzowano wszystkie drzewa, w których liczby dominowania powściągniętego oraz podwójnie totalnego są sobie równe.

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