Temat: 2-domination - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Trees whose 2-domination subdivision number is 2
Autorzy:: Atapour, M.
Sheikholeslami, S. M.
Khodkar, A.
Powiązania:: https://bibliotekanauki.pl/articles/254847.pdf
Data publikacji:: 2012
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: 2-dominating set
2-domination number
2-domination subdivision numbe
Opis:: A set S of vertices in a graph G = (V,E) is a 2-dominating set if every vertex of V \ S is adjacent to at least two vertices of S. The 2-domination number of a graph G, denoted by γ2(G), is the minimum size of a 2-dominating set of G. The 2-domination subdivision number sdγ2 (G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the 2-domination number. The authors have recently proved that for any tree T of order at least 3, 1 ≤ sdγ2 (T ) ≤ 2. In this paper we provide a constructive characterization of the trees whose 2-domination subdivision number is 2.
Źródło:: Opuscula Mathematica; 2012, 32, 3; 423-437
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Bounds on the 2-domination number in cactus graphs
Autorzy:: Chellali, M.
Powiązania:: https://bibliotekanauki.pl/articles/254915.pdf
Data publikacji:: 2006
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: 2-domination number
total domination number
independence number
cactus graphs
trees
Opis:: A 2-dominating set of a graph G is a set D of vertices of G such that every vertex not in S is dominated at least twice. The minimum cardinality of a 2-dominating set of G is the 2-domination number γ2(G). We show that if G is a nontrivial connected cactus graph with k(G) even cycles (k(G) ≥ 0), then γ2(G) ≥ γt(G) - k(G), and if G is a graph of order n with at most one cycle, then γ2(G) ≥ (n + l - s)/2 improving Fink and Jacobson's lower bound for trees with l > s, where γt(G), l and s are the total domination number, the number of leaves and support vertices of G, respectively. We also show that if T is a tree of order n ≥ 3, then γ2(T) ≤ β(T) + s - 1, where β(T) is the independence number of T.
Źródło:: Opuscula Mathematica; 2006, 26, 1; 5-12
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Criticality indices of 2-rainbow domination of paths and cycles
Autorzy:: Bouchou, A.
Blidia, M.
Powiązania:: https://bibliotekanauki.pl/articles/255150.pdf
Data publikacji:: 2016
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: 2-rainbow domination number
criticality index
Opis:: A 2-rainbow dominating function of a graph G (V(G), E(G)) is a function ƒ that assigns to each vertex a set of colors chosen from the set {1,2} so that for each vertex with ƒ (v) = ∅ we have [formula].The weight of a 2RDF ƒ is defined as [formula] minimum weight of a 2RDF is called the 2-rainbow domination number of G, denoted by [formula].The vertex criticality index of a 2-rainbow domination of a graph G is defined as [formula] the edge removal criticality index of a 2-rainbow domination of a graph G is defined as [formula] and the edge addition of a 2-rainbow domination criticality index of G is defined as [formula] where G is the complement graph of G. In this paper, we determine the criticality indices of paths and cycles.
Źródło:: Opuscula Mathematica; 2016, 36, 5; 563-574
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: On 2-rainbow domination number of functigraph and its complement
Autorzy:: Shaminezhad, Athena
Vatandoost, Ebrahim
Powiązania:: https://bibliotekanauki.pl/articles/255140.pdf
Data publikacji:: 2020
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: 2-rainbow domination number
functigraph
complement
cubic graph
Opis:: Let G be a graph and ƒ : V(G) → P({1, 2}) be a function where for every vertex v ∈ V(G), with ƒ (v) = ∅ we have [formula]. Then ƒ is a 2-rainbow dominating function or a 2RDF of G. The weight of ƒ is[formula]. The minimum weight of all 2-rainbow dominating functions is 2-rainbow domination number of G, denoted by [formula]. Let G 1 and G2 be two copies of a graph G with disjoint vertex sets V(G 1) and V(G2), and let σ be a function from V(G 1) to V(G2). We define the functigraph C(G,σ) to be the graph that has the vertex set V(C(G, ,σ)) = V(G 1) U V(G2), and the edge set [formula]. In this paper, 2-rainbow domination number of the functigraph of C(G, ,σ) and its complement are investigated. We obtain a general bound for [formula] and we show that this bound is sharp.
Źródło:: Opuscula Mathematica; 2020, 40, 5; 617-627
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 5.

Tytuł:: On minimum intersections of certain secondary dominating sets in graphs
Autorzy:: Kosiorowska, Anna
Michalski, Adrian
Włoch, Iwona
Powiązania:: https://bibliotekanauki.pl/articles/29519420.pdf
Data publikacji:: 2023
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: dominating set
2-dominating set
(1, 2)-dominating set
proper (1, 2)-dominating set
domination number
(1,2)-intersection index
Opis:: In this paper we consider secondary dominating sets, also named as (1,k)-dominating sets, introduced by Hedetniemi et al. in 2008. In particular, we study intersections of the (1, 1)-dominating sets and proper (1, 2)-dominating sets. We introduce (1,2̅)-intersection index as the minimum possible cardinality of such intersection and determine its value for some classes of graphs.
Źródło:: Opuscula Mathematica; 2023, 43, 6; 813-827
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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