Autor: Chen, Xue-Gang - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Trees with equal total domination and total restrained domination numbers
Autorzy:: Chen, Xue-Gang
Shiu, Wai
Chen, Hong-Yu
Powiązania:: https://bibliotekanauki.pl/articles/743513.pdf
Data publikacji:: 2008
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: total domination number
total restrained domination number
tree
Opis:: For a graph G = (V,E), a set S ⊆ V(G) is a total dominating set if it is dominating and both ⟨S⟩ has no isolated vertices. The cardinality of a minimum total dominating set in G is the total domination number. A set S ⊆ V(G) is a total restrained dominating set if it is total dominating and ⟨V(G)-S⟩ has no isolated vertices. The cardinality of a minimum total restrained dominating set in G is the total restrained domination number. We characterize all trees for which total domination and total restrained domination numbers are the same.
Źródło:: Discussiones Mathematicae Graph Theory; 2008, 28, 1; 59-66
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Hereditary Equality of Domination and Exponential Domination in Subcubic Graphs
Autorzy:: Chen, Xue-Gang
Wang, Yu-Feng
Wu, Xiao-Fei
Powiązania:: https://bibliotekanauki.pl/articles/32324524.pdf
Data publikacji:: 2021-11-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: dominating set
exponential dominating set
subcubic graphs
Opis:: Let γ(G) and γ_e(G) denote the domination number and exponential domination number of graph G, respectively. Henning et al., in [Hereditary equality of domination and exponential domination, Discuss. Math. Graph Theory 38 (2018) 275–285] gave a conjecture: There is a finite set ℱ of graphs such that a graph G satisfies (H) = γ_e(H) for every induced subgraph H of G if and only if G is ℱ-free. In this paper, we study the conjecture for subcubic graphs. We characterize the class ℱ by minimal forbidden induced subgraphs and prove that the conjecture holds for subcubic graphs.
Źródło:: Discussiones Mathematicae Graph Theory; 2021, 41, 4; 1067-1075
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: On the total restrained domination number of direct products of graphs
Autorzy:: Shiu, Wai
Chen, Hong-Yu
Chen, Xue-Gang
Sun, Pak
Powiązania:: https://bibliotekanauki.pl/articles/743278.pdf
Data publikacji:: 2012
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: total domination number
total restrained domination number
direct product of graphs
Opis:: Let G = (V,E) be a graph. A total restrained dominating set is a set S ⊆ V where every vertex in V∖S is adjacent to a vertex in S as well as to another vertex in V∖S, and every vertex in S is adjacent to another vertex in S. The total restrained domination number of G, denoted by $γ_r^t(G)$, is the smallest cardinality of a total restrained dominating set of G. We determine lower and upper bounds on the total restrained domination number of the direct product of two graphs. Also, we show that these bounds are sharp by presenting some infinite families of graphs that attain these bounds.
Źródło:: Discussiones Mathematicae Graph Theory; 2012, 32, 4; 629-641
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

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