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Wyświetlanie 1-15 z 21
Tytuł:
The graph theory approach to analyze critical infrastructures of transportation systems
Autorzy:
Guze, S.
Powiązania:
https://bibliotekanauki.pl/articles/2069516.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Morski w Gdyni. Polskie Towarzystwo Bezpieczeństwa i Niezawodności
Tematy:
critical infrastructures
domination set
domination number
minimal spanning tree
Opis:
The main aim of the paper is to use algorithms and parameters of graph theory as tool to analyze the transpiration systems. To realize this goal the well-known information about graph theory algorithms and parameters will be introduced and described. The possible application of graph theory algorithms and parameters to analyze the critical infrastructures of exemplary transportation system will be shown.
Źródło:
Journal of Polish Safety and Reliability Association; 2014, 5, 2; 57--62
2084-5316
Pojawia się w:
Journal of Polish Safety and Reliability Association
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Efficient Domination in Cayley Graphs of Generalized Dihedral Groups
Autorzy:
Caliskan, Cafer
Miklavič, Štefko
Özkan, Sibel
Šparl, Primož
Powiązania:
https://bibliotekanauki.pl/articles/32304153.pdf
Data publikacji:
2022-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
efficient domination set
Cayley graph
generalized dihedral group
Opis:
An independent subset D of the vertex set V of the graph Γ is an efficient dominating set for Γ if each vertex v ∈ V \ D has precisely one neighbour in D. In this article, we classify the connected cubic Cayley graphs on generalized dihedral groups which admit an efficient dominating set.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 3; 823-841
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Independent set dominanting sets in bipartite graphs
Autorzy:
Zelinka, B.
Powiązania:
https://bibliotekanauki.pl/articles/255203.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
set dominanting set
set domination number
independent set
bipartite graph
multihypergraph
Opis:
The paper continues the study of independent set dominating sets in graphs which was started by E. Sampathkumar. A subset D of the vertex set V(G) of a graph G is called a set dominating set (shortly sd-set) in G, if for each set X ikkeq V(G) - D there exists a set Y ikkeq D such that the subgraph of G induced X cup Y is connected. The minimum number of vertices of an sd-set in G is called the set domination number gammas (G) of G. An sd-set D in G such that /D/ = gammas(G) is called a gammas-set in G. In this paper we study sd-sets in bipartite graphs which are simultaneously independent. We apply the theory of hypergraphs.
Źródło:
Opuscula Mathematica; 2005, 25, 2; 345-349
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Odd and residue domination numbers of a graph
Autorzy:
Caro, Yair
Klostermeyer, William
Goldwasser, John
Powiązania:
https://bibliotekanauki.pl/articles/743442.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
dominating set
odd dominating set
parity domination
Opis:
Let G = (V,E) be a simple, undirected graph. A set of vertices D is called an odd dominating set if |N[v] ∩ D| ≡ 1 (mod 2) for every vertex v ∈ V(G). The minimum cardinality of an odd dominating set is called the odd domination number of G, denoted by γ₁(G). In this paper, several algorithmic and structural results are presented on this parameter for grids, complements of powers of cycles, and other graph classes as well as for more general forms of "residue" domination.
Źródło:
Discussiones Mathematicae Graph Theory; 2001, 21, 1; 119-136
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On equality in an upper bound for the acyclic domination number
Autorzy:
Samodivkin, V.
Powiązania:
https://bibliotekanauki.pl/articles/255046.pdf
Data publikacji:
2008
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
dominating set
acyclic set
independent set
acyclic domination number
Opis:
A subset A of vertices in a graph G is acyclic if the subgraph it induces contains no cycles. The acyclic domination number ϒa (G) of a graph G is the minimum cardinality of an acyclic dominating set of G. For any graph G with n vertices and maximum degree Δ(G), ϒa(G) ≤ n - Δ(G). In this paper we characterize the connected graphs and the connected triangle-free graphs which achieve this upper bound.
Źródło:
Opuscula Mathematica; 2008, 28, 3; 331-334
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Highly connected counterexamples to a conjecture on α-domination
Autorzy:
Tuza, Zsolt
Powiązania:
https://bibliotekanauki.pl/articles/744177.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
dominating set
α-domination
Opis:
An infinite class of counterexamples is given to a conjecture of Dahme et al. [1] concerning the minimum size of a dominating vertex set that contains at least a prescribed proportion of the neighbors of each vertex not belonging to the set.
Źródło:
Discussiones Mathematicae Graph Theory; 2005, 25, 3; 435-440
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weakly convex and convex domination numbers
Autorzy:
Lemańska, M.
Powiązania:
https://bibliotekanauki.pl/articles/2050775.pdf
Data publikacji:
2004
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
dominating set
connected domination number
distance
isometric set
convex set
Opis:
Two new domination parameters for a connected graph G: the weakly convex domination number of G and the convex domination number of G are introduced. Relations between these parameters and the other domination parameters are derived. In particular, we study for which cubic graphs the convex domination number equals the connected domination number.
Źródło:
Opuscula Mathematica; 2004, 24, 2; 181-188
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
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
Tytuł:
Graph domination in distance two
Autorzy:
Bacsó, Gábor
Tálos, Attila
Tuza, Zsolt
Powiązania:
https://bibliotekanauki.pl/articles/744316.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
dominating set
connected domination
distance domination
forbidden induced subgraph
Opis:
Let G = (V,E) be a graph, and k ≥ 1 an integer. A subgraph D is said to be k-dominating in G if every vertex of G-D is at distance at most k from some vertex of D. For a given class of graphs, Domₖ is the set of those graphs G in which every connected induced subgraph H has some k-dominating induced subgraph D ∈ which is also connected. In our notation, Dom coincides with Dom₁. In this paper we prove that $Dom Dom _u = Dom₂ _u$ holds for $_u$ = {all connected graphs without induced $P_u$} (u ≥ 2). (In particular, ₂ = {K₁} and ₃ = {all complete graphs}.) Some negative examples are also given.
Źródło:
Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 121-128
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The domination number of $K_n^3$
Autorzy:
Georges, John
Lin, Jianwei
Mauro, David
Powiązania:
https://bibliotekanauki.pl/articles/30148694.pdf
Data publikacji:
2014-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Cartesian product
dominating set
domination number
Opis:
Let $K_n^3$ denote the Cartesian product $K_n□K_n□K_n$, where $K_n$ is the complete graph on $n$ vertices. We show that the domination number of $K_n^3$ is $⌈\frac{n^2}{2}⌉$.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 3; 629-632
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Domination Number of Graphs with Minimum Degree Five
Autorzy:
Bujtás, Csilla
Powiązania:
https://bibliotekanauki.pl/articles/32222697.pdf
Data publikacji:
2021-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
dominating set
domination number
discharging method
Opis:
We prove that for every graph G on n vertices and with minimum degree five, the domination number γ(G) cannot exceed n/3. The proof combines an algorithmic approach and the discharging method. Using the same technique, we provide a shorter proof for the known upper bound 4n/11 on the domination number of graphs of minimum degree four.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 3; 763-777
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dominating sets and domination polynomials of certain graphs, II
Autorzy:
Alikhani, S.
Yee-hock, P.
Powiązania:
https://bibliotekanauki.pl/articles/255942.pdf
Data publikacji:
2010
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
domination polynomial
dominating set
cycle
theta graph
Opis:
The domination polynomial of a graph G of order n is the polynomial [formula] where d(G, i) is the number of dominating sets of G of size i, and ϒ (G) is the domination number of G. In this paper, we obtain some properties of the coefficients of D(G, x). Also, by study of the dominating sets and the domination polynomials of specific graphs denoted by G'(m), we obtain a relationship between the domination polynomial of graphs containing an induced path of length at least three, and the domination polynomial of related graphs obtained by replacing the path by shorter path. As examples of graphs G' (m), we study the dominating sets and domination polynomials of cycles and generalized theta graphs. Finally, we show that, if n ≡ 0, 2(mod 3) and D(G, x) = D(Cn, x), then G = Cn.
Źródło:
Opuscula Mathematica; 2010, 30, 1; 37-51
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Domination in partitioned graphs
Autorzy:
Tuza, Zsolt
Vestergaard, Preben
Powiązania:
https://bibliotekanauki.pl/articles/743565.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
dominating set
domination number
vertex partition
Opis:
Let V₁, V₂ be a partition of the vertex set in a graph G, and let $γ_i$ denote the least number of vertices needed in G to dominate $V_i$. We prove that γ₁+γ₂ ≤ [4/5]|V(G)| for any graph without isolated vertices or edges, and that equality occurs precisely if G consists of disjoint 5-paths and edges between their centers. We also give upper and lower bounds on γ₁+γ₂ for graphs with minimum valency δ, and conjecture that γ₁+γ₂ ≤ [4/(δ+3)]|V(G)| for δ ≤ 5. As δ gets large, however, the largest possible value of (γ₁+γ₂)/|V(G)| is shown to grow with the order of (logδ)/(δ).
Źródło:
Discussiones Mathematicae Graph Theory; 2002, 22, 1; 199-210
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Counterexample to a conjecture on the structure of bipartite partitionable graphs
Autorzy:
Gibson, Richard
Mynhardt, Christina
Powiązania:
https://bibliotekanauki.pl/articles/743437.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination
prism fixer
symmetric dominating set
bipartite graph
Opis:
A graph G is called a prism fixer if γ(G×K₂) = γ(G), where γ(G) denotes the domination number of G. A symmetric γ-set of G is a minimum dominating set D which admits a partition D = D₁∪ D₂ such that $V(G)-N[D_i] = D_j$, i,j = 1,2, i ≠ j. It is known that G is a prism fixer if and only if G has a symmetric γ-set.
Hartnell and Rall [On dominating the Cartesian product of a graph and K₂, Discuss. Math. Graph Theory 24 (2004), 389-402] conjectured that if G is a connected, bipartite graph such that V(G) can be partitioned into symmetric γ-sets, then G ≅ C₄ or G can be obtained from $K_{2t,2t}$ by removing the edges of t vertex-disjoint 4-cycles. We construct a counterexample to this conjecture and prove an alternative result on the structure of such bipartite graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 3; 527-540
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal Locating-Total Dominating Sets in Strips of Height 3
Autorzy:
Junnila, Ville
Powiązania:
https://bibliotekanauki.pl/articles/31339416.pdf
Data publikacji:
2015-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
locating-total dominating set
domination
square grid
strip
Opis:
A set C of vertices in a graph G = (V,E) is total dominating in G if all vertices of V are adjacent to a vertex of C. Furthermore, if a total dominating set C in G has the additional property that for any distinct vertices u, v ∈ V \ C the subsets formed by the vertices of C respectively adjacent to u and v are different, then we say that C is a locating-total dominating set in G. Previously, locating-total dominating sets in strips have been studied by Henning and Jafari Rad (2012). In particular, they have determined the sizes of the smallest locating-total dominating sets in the finite strips of height 2 for all lengths. Moreover, they state as open question the analogous problem for the strips of height 3. In this paper, we answer the proposed question by determining the smallest sizes of locating-total dominating sets in the finite strips of height 3 as well as the smallest density in the infinite strip of height 3.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 3; 447-462
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 21

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