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Wyświetlanie 1-15 z 43
Tytuł:
Neighbourhood total domination in graphs
Autorzy:
Arumugam, S.
Sivagnanam, C.
Powiązania:
https://bibliotekanauki.pl/articles/254824.pdf
Data publikacji:
2011
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
neighbourhood total domination
total domination
connected domination
paired domination
neighbourhood total domatic number
Opis:
Let G = (V, E) be a graph without isolated vertices. A dominating set S of G is called a neighbourhood total dominating set (ntd-set) if the induced subgraph ⟨ N(S) ⟩ has no isolated vertices. The minimum cardinality of a ntd-set of G is called the neighbourhood total domination number of G and is denoted by ϒnt(G). The maximum order of a partition of V into ntd-sets is called the neighbourhood total domatic number of G and is denoted by dnt(G). In this paper we initiate a study of these parameters.
Źródło:
Opuscula Mathematica; 2011, 31, 4; 519-531
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The paired-domination and the upper paired-domination numbers of graphs
Autorzy:
Ulatowski, W.
Powiązania:
https://bibliotekanauki.pl/articles/255585.pdf
Data publikacji:
2015
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
paired-domination
paired-domination number
upper paired-domination number
Opis:
In this paper we continue the study of paired-domination in graphs. A paired-dominating set, abbreviated PDS, of a graph G with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G, denoted by γP(G), is the minimum cardinality of a PDS of G. The upper paired-domination number of G, denoted by ΓP(G), is the maximum cardinality of a minimal PDS of G. Let G be a connected graph of order n ≥ 3. Haynes and Slater in [Paired-domination in graphs, Networks 32 (1998), 199-206], showed that γ P(G) ≤ n— 1 and they determine the extremal graphs G achieving this bound. In this paper we obtain analogous results for ΓP(G). Dorbec, Henning and McCoy in [Upper total domination versus upper paired-domination, Questiones Mathematicae 30 (2007), 1-12] determine Γp(Pn), instead in this paper we determine Γp(Cn). Moreover, we describe some families of graphs G for which the equality γP(G) = ΓP(G) holds.
Źródło:
Opuscula Mathematica; 2015, 35, 1; 127-135
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On domination multisubdivision number of unicyclic graphs
Autorzy:
Raczek, J.
Powiązania:
https://bibliotekanauki.pl/articles/255095.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
domination number
domination subdivision number
domination multisubdivision number
trees
unicyclic graphs
Opis:
The paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009), 622-628], we constructively characterize all connected unicyclic graphs with the domination multisubdivision number equal to 3. We end with further questions and open problems.
Źródło:
Opuscula Mathematica; 2018, 38, 3; 409-425
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bounds on perfect k-domination in trees: an algorithmic approach
Autorzy:
Chaluvaraju, B.
Vidya, K. A.
Powiązania:
https://bibliotekanauki.pl/articles/255985.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
k-domination
perfect domination
perfect k-domination
Opis:
Let k be a positive integer and G = (V, E) be a graph. A vertex subset D of a graph G is called a perfect k-dominating set of G if every vertex v of G not in D is adjacent to exactly k vertices of D. The minimum cardinality of a perfect k -dominating set of G is the perfect k-domination number γkp (G ). In this paper, a sharp bound for γkp (T) is obtained where T is a tree.
Źródło:
Opuscula Mathematica; 2012, 32, 4; 707-714
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Graphs with equal domination and certified domination numbers
Autorzy:
Dettlaff, Magda
Lemańska, Magdalena
Miotk, Mateusz
Topp, Jerzy
Ziemann, Radosław
Żyliński, Paweł
Powiązania:
https://bibliotekanauki.pl/articles/255932.pdf
Data publikacji:
2019
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
domination
certified domination
Opis:
A set D of vertices of a graph G = (VG, EG) is a dominating set of G if every vertex in VG — D is adjacent to at least one vertex in D. The domination number (upper domination number, respectively) of G, denoted by [formula], respectively), is the cardinality of a smallest (largest minimal, respectively) dominating set of G. A subset D ⊆ VG is called a certified dominating set of G if D is a dominating set of G and every vertex in D has either zero or at least two neighbors in VG — D. The cardinality of a smallest (largest minimal, respectively) certified dominating set of G is called the certified (upper certified, respectively) domination number of G and is denoted by [formula]), respectively). In this paper relations between domination, upper domination, certified domination and upper certified domination numbers of a graph are studied.
Źródło:
Opuscula Mathematica; 2019, 39, 6; 815-827
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Domination parameters of a graph with added vertex
Autorzy:
Zwierzchowski, M.
Powiązania:
https://bibliotekanauki.pl/articles/2050876.pdf
Data publikacji:
2004
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
total domination number
strong domination number
subdivision
Opis:
Let $G = (V, E)$ be a graph. A subset $D \subseteq V$ is a total dominating set of $G$ if for every vertex $y \in V$ there is a vertex $x \in D$ with $xy \in E$. A subset $D \subseteq V$ is a strong dominating set of G if for every vertex $y \in V - D$ there is a vertex $x \in D$ with $xy \in E and deg_{G}(x) \geq deg_{G}(y)$. The total domination number $\gamma_{t}(G)$ (the strong domination number $\gamma_{S}(G)$) is defined as the minimum cardinality of a total dominating set (a strong dominating set) of $G$. The concept of total domination was first defined by Cockayne, Dawes and Hedetniemi in 1980 [1], while the strong domination was introduced by Sampathkumar and Pushpa Latha in 1996 [3]. By a subdivision of an edge $uv \in E$ we mean removing edge $uv$, adding a new vertex $x$, and adding edges $ux$ and $vx$. A graph obtained from $G$ by subdivision an edge $uv \in E$ is denoted by $G \oplus uxvx$. The behaviour of the total domination number and the strong domination number of a graph $G \oplus u_{x}v_{x}$ is developed.
Źródło:
Opuscula Mathematica; 2004, 24, 2; 231-234
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
All graphs with paired-domination number two less than their order
Autorzy:
Ulatowski, W.
Powiązania:
https://bibliotekanauki.pl/articles/255220.pdf
Data publikacji:
2013
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
paired-domination
paired-domination number
Opis:
Let G = (V,E) be a graph with no isolated vertices. A set S ⊆ V is a paired-dominating set of G if every vertex not in S is adjacent with some vertex in S and the subgraph induced by S contains a perfect matching. The paired-domination number Υρ (G) of G is defined to be the minimum cardinality of a paired-dominating set of G. Let G be a graph of order n. In [Paired-domination in graphs, Networks 32 (1998), 199–206] Haynes and Slater described graphs G with Υρ (G) = n and also graphs with Υρ (G) = n − 1. In this paper we show all graphs for which Υρ (G) = n − 2.
Źródło:
Opuscula Mathematica; 2013, 33, 4; 763-783
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
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
Tytuł:
An upper bound on the total outer-independent domination number of a tree
Autorzy:
Krzywkowski, M.
Powiązania:
https://bibliotekanauki.pl/articles/255991.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
total outer-independent domination
total domination
tree
Opis:
A total outer-independent dominating set of a graph G = (V (G),E(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, denoted by [formula], is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every tree T of order n ≥ 4, with l leaves and s support vertices we have [formula], and we characterize the trees attaining this upper bound.
Źródło:
Opuscula Mathematica; 2012, 32, 1; 153-158
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on the independent Roman domination in unicyclic graphs
Autorzy:
Chellali, M.
Rad, N. J.
Powiązania:
https://bibliotekanauki.pl/articles/255989.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Roman domination
independent Roman domination
strong equality
Opis:
A Roman dominating function (RDF) on a graph G= (V, E) is a function ƒ : V → {0, 1, 2} satisfying the condition that every vertex u for which ƒ(u) = 0 is adjacent to at least one vertex v for which ƒ(v)=2. The weight of an RDF is the value [formula]. An RDF ƒ in a graph G is independent if no two vertices assigned positive values are adjacent. The Roman domination number ΥR (G) (respectively, the independent Roman domination number ΥR(G) is the minimum weight of an RDF (respectively, independent RDF) on G. We say that ΥR(G) strongly equals iR(G), denoted by ΥR(G) ≡ iR(G), if every RDF on G of minimum weight is independent. In this note we characterize all unicyclic graphs G with ΥR(G) ≡ iR(G).
Źródło:
Opuscula Mathematica; 2012, 32, 4; 715-718
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs
Autorzy:
Dettlaff, M.
Raczek, J.
Yero, I. G.
Powiązania:
https://bibliotekanauki.pl/articles/255785.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
domination
paired domination
independent domination
edge subdivision
edge multisubdivision
corona graph
Opis:
Given a graph G = (V, E), the subdivision of an edge e = uv ∈ E(G) means the substitution of the edge e by a vertex x and the new edges ux and xv. The domination subdivision number of a graph G is the minimum number of edges of G which must be subdivided (where each edge can be subdivided at most once) in order to increase the domination number. Also, the domination multisubdivision number of G is the minimum number of subdivisions which must be done in one edge such that the domination number increases. Moreover, the concepts of paired domination and independent domination subdivision (respectively multisubdivision) numbers are denned similarly. In this paper we study the domination, paired domination and independent domination (subdivision and multisubdivision) numbers of the generalized corona graphs.
Źródło:
Opuscula Mathematica; 2016, 36, 5; 575-588
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Total connected domination game
Autorzy:
Bujtás, Csilla
Henning, Michael A.
Iršič, Vesna
Klavžar, Sandi
Powiązania:
https://bibliotekanauki.pl/articles/2050904.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
connected domination game
total connected domination game
graph product
tree
Opis:
The (total) connected domination game on a graph $G$ is played by two players, Dominator and Staller, according to the standard (total) domination game with the additional requirement that at each stage of the game the selected vertices induce a connected subgraph of $G$. If Dominator starts the game and both players play optimally, then the number of vertices selected during the game is the (total) connected game domination number $(\gamma_{tcg}(G))(\gamma_{cg(G)})$ of $G$. We show that $\gamma_{tcg}(G) \in \{\gamma_{cg}(G), \gamma_{cg}(G)+1, \gamma_{cg}(G)+2\}$, and consequently define $G$ as Class $i$ if $\gamma_{tcg}(G) = \gamma_{cg}(G)+i$ for $i \in \{0, 1, 2\}$. A large family of Class 0 graphs is constructed which contains all connected Cartesian product graphs and connected direct product graphs with minimum degree at least 2. We show that no tree is Class 2 and characterize Class 1 trees. We provide an infinite family of Class 2 bipartite graphs.
Źródło:
Opuscula Mathematica; 2021, 41, 4; 453-464
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on a relation between the weak and strong domination numbers of a graph
Autorzy:
Boutrig, R.
Chellali, M.
Powiązania:
https://bibliotekanauki.pl/articles/255983.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
weak domination
strong domination
Opis:
In a graph G = (V, E) a vertex is said to dominate itself and all its neighbors. A set D ⊆ V is a weak (strong, respectively) dominating set of G if every vertex v ∈ V - S is adjacent to a vertex u ∈ D such that dG(v) ≥ dG(u) (dG(v) ≤ dG(u), respectively). The weak (strong, respectively) domination number of G, denoted by ϒw(G) (ϒs(G), respectively), is the minimum cardinality of a weak (strong, respectively) dominating set of G. In this note we show that if G is a connected graph of order n ≥ 3, then ϒw(G) + tϒs(G) ≤ n, where t = 3/(Δ+1) if G is an arbitrary graph, t = 3/5 if G is a block graph, and t = 2/3 if G is a claw free graph.
Źródło:
Opuscula Mathematica; 2012, 32, 2; 235-238
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on bipartite graphs whose [1, k]-domination number equal to their number of vertices
Autorzy:
Ghareghani, Narges
Peterin, Iztok
Sharifani, Pouyeh
Powiązania:
https://bibliotekanauki.pl/articles/256007.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
domination
[1, k]-domination number
[l,k]-total domination number
bipartite graphs
Opis:
A subset D of the vertex set V of a graph G is called an [1, k]-dominating set if every vertex from V — D is adjacent to at least one vertex and at most fc vertices of D. A [1, k]-dominating set with the minimum number of vertices is called a [formula]-set and the number of its vertices is the [1, k]-domination number [formula] of G. In this short note we show that the decision problem whether [formula] is an NP-hard problem, even for bipartite graphs. Also, a simple construction of a bipartite graph G of order n satisfying [formula] is given for every integer n ≥ (k + l)(2k + 3).
Źródło:
Opuscula Mathematica; 2020, 40, 3; 375-382
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Remarks on the outer-independent double Italian domination number
Autorzy:
Volkman, Lutz
Powiązania:
https://bibliotekanauki.pl/articles/2051048.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
double Italian domination number
outer-independent double Italian domination number
Nordhaus-Gaddum bound
Opis:
Let $G$ be a graph with vertex set $V(G)$. If $u \in V(G)$, then $N[u]$ is the closed neighborhood of $u$. An outer-independent double Italian dominating function (OIDIDF) on a graph $G$ is a function $ƒ : V(G) \rightarrow \{0, 1, 2, 3\}$ such that if $ƒ (v) \in \{0, 1\}$ for a vertex $v \in V(G)$, then $\Sigma_{x \in N[v]} f(x) \geq 3$, and the set ${u \in V(G) : f (u) = 0}$ is independent. The weight of an OIDIDF $f$ is the sum $\Sigma_{v \in V(G)} f(v)$. The outer-independent double Italian domination number $\gamma_{oidI}(G)$ equals the minimum weight of an OIDIDF on G. In this paper we present Nordhaus-Gaddum type bounds on the outer-independent double Italian domination number which improved corresponding results given in [F. Azvin, N. Jafari Rad, L. Volkmann, \textit{Bounds on the outer-independent double Italian domination number}, Commun. Comb. Optim. 6 (2021), 123-136]. Furthermore, we determine the outer-independent double Italian domination number of some families of graphs.
Źródło:
Opuscula Mathematica; 2021, 41, 2; 259-268
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 43

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