Temat: k -tuple total domination

Skocz do pozycji: 1.

Tytuł:: On the Total k-Domination in Graphs
Autorzy:: Bermudo, Sergio
Hernández-Gómez, Juan C.
Sigarreta, José M.
Tematy:: k -domination
total k -domination
k -tuple domination
k -tuple total domination; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31342422.pdf Link otwiera się w nowym oknie
Opis:: Let G=(V, E) be a graph; a set S ⊆ V is a total k-dominating set if every vertex v ∈ V has at least k neighbors in S. The total k-domination number γ_kt(G) is the minimum cardinality among all total k-dominating sets. In this paper we obtain several tight bounds for the total k-domination number of a graph. In particular, we investigate the relationship between the total k-domination number of a graph and the order, the size, the girth, the minimum and maximum degree, the diameter, and other domination parameters of the graph.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: On the total k-domination number of graphs
Autorzy:: Kazemi, Adel
Tematy:: total k-domination (k-tuple total domination) number
k-tuple domination number
k-transversal number; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743228.pdf Link otwiera się w nowym oknie
Opis:: Let k be a positive integer and let G = (V,E) be a simple graph. The k-tuple domination number $γ_{×k}(G)$ of G is the minimum cardinality of a k-tuple dominating set S, a set that for every vertex v ∈ V, $|N_G[v] ∩ S| ≥ k$. Also the total k-domination number $γ_{×k,t}(G)$ of G is the minimum cardinality of a total k -dominating set S, a set that for every vertex v ∈ V, $|N_G(v) ∩ S| ≥ k$. The k-transversal number τₖ(H) of a hypergraph H is the minimum size of a subset S ⊆ V(H) such that |S ∩e | ≥ k for every edge e ∈ E(H).
We know that for any graph G of order n with minimum degree at least k, $γ_{×k}(G) ≤ γ_{×k,t}(G) ≤ n$. Obviously for every k-regular graph, the upper bound n is sharp. Here, we give a sufficient condition for $γ_{×k,t}(G) < n$. Then we characterize complete multipartite graphs G with $γ_{×k}(G) = γ_{×k,t}(G)$. We also state that the total k-domination number of a graph is the k -transversal number of its open neighborhood hypergraph, and also the domination number of a graph is the transversal number of its closed neighborhood hypergraph. Finally, we give an upper bound for the total k -domination number of the cross product graph G×H of two graphs G and H in terms on the similar numbers of G and H. Also, we show that this upper bound is strict for some graphs, when k = 1.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: On the inverse signed total domination number in graphs
Autorzy:: Mojdeh, D. A.
Samadi, B.
Tematy:: inverse signed total dominating function
inverse signed total domination number
k-tuple total domination number; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/255392.pdf Link otwiera się w nowym oknie
Opis:: In this paper, we study the inverse signed total domination number in graphs and present new sharp lower and upper bounds on this parameter. For example by making use of the classic theorem of Turán (1941), we present a sharp upper bound on Kr+1-free graphs for r ≥ 2. Also, we bound this parameter for a tree from below in terms of its order and the number of leaves and characterize all trees attaining this bound.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: 3-Tuple Total Domination Number of Rook’s Graphs
Autorzy:: Pahlavsay, Behnaz
Palezzato, Elisa
Torielli, Michele
Tematy:: k -tuple total domination
Cartesian product of graphs
rook’s graph
Vizing’s conjecture; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/32361755.pdf Link otwiera się w nowym oknie
Opis:: A k-tuple total dominating set (kTDS) of a graph G is a set S of vertices in which every vertex in G is adjacent to at least k vertices in S. The minimum size of a kTDS is called the k-tuple total dominating number and it is denoted by γ_×k,t(G). We give a constructive proof of a general formula for γ_×3,t(K_n□K_m).
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Some results on total domination in direct products of graphs
Autorzy:: Dorbec, Paul
Gravier, Sylvain
Klavžar, Sandi
Spacapan, Simon
Tematy:: direct product
total domination
k-tuple domination
open packing
domination; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743885.pdf Link otwiera się w nowym oknie
Opis:: Upper and lower bounds on the total domination number of the direct product of graphs are given. The bounds involve the {2}-total domination number, the total 2-tuple domination number, and the open packing number of the factors. Using these relationships one exact total domination number is obtained. An infinite family of graphs is constructed showing that the bounds are best possible. The domination number of direct products of graphs is also bounded from below.
Dostawca treści:: Biblioteka Nauki

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