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Wyświetlanie 1-15 z 327
Tytuł:
The domination over time and its discretisation
Autorzy:
Abbasnezhad, Nazanin
Mehri-Takmeh, Javad
Vakili, Javad
Powiązania:
https://bibliotekanauki.pl/articles/406615.pdf
Data publikacji:
2020
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
domination over time
continuous linear programming
duality
discretisation
Opis:
Domination in graphs is well known and has been an extensively researched branch of graph theory. Since the variation over time is one of the important properties of real-world networks, we study the influence of time on the domination problem. In this paper, we introduce the domination over time problem, including time delay on arcs. Then, an optimal solution to its discretisation is obtained, which is the solution of the original problem.
Źródło:
Operations Research and Decisions; 2020, 30, 1; 5-24
2081-8858
2391-6060
Pojawia się w:
Operations Research and Decisions
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Independent Domination in Planar Cubic Graphs
Autorzy:
Abrishami, Gholamreza
Henning, Michael A.
Rahbarnia, Freydoon
Powiązania:
https://bibliotekanauki.pl/articles/31343229.pdf
Data publikacji:
2019-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
independent domination number
domination number
cubic graphs
Opis:
A set $S$ of vertices in a graph $G$ is an independent dominating set of $G$ if $S$ is an independent set and every vertex not in $S$ is adjacent to a vertex in $S$. The independent domination number, $i(G)$, of $G$ is the minimum cardinality of an independent dominating set. Goddard and Henning [Discrete Math. 313 (2013) 839–854] posed the conjecture that if \( G \not\in \{ K_{3,3}, C_5 \square K_2 \} \) is a connected, cubic graph on $n$ vertices, then $i(G) \le 3/8 n $, where $ C_5 \square K_2 $ is the 5-prism. As an application of known result, we observe that this conjecture is true when $G$ is 2-connected and planar, and we provide an infinite family of such graphs that achieve the bound. We conjecture that if $G$ is a bipartite, planar, cubic graph of order $n$, then $ i(G) \le 1/3 n $, and we provide an infinite family of such graphs that achieve this bound.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 4; 841-853
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weak and exact domination in distributed systems
Autorzy:
Afifi, L.
Magri, E. M.
El Jai, A.
Powiązania:
https://bibliotekanauki.pl/articles/907699.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
system rozproszony
dominacja
aktuator
czujnik
distributed system
domination
actuators
sensors
Opis:
In this work, we introduce and examine the notion of domination for a class of linear distributed systems. This consists in studying the possibility to make a comparison between input or output operators. We give the main algebraic properties of such relations, as well as characterizations of exact and weak domination. We also study the case of actuators, and various situations are examined. Applications and illustrative examples are also given. By duality, we extend this study to observed systems. We obtain similar results and properties, and the case of sensors is equally examined.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2010, 20, 3; 419-426
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Total 2-Rainbow Domination Numbers of Trees
Autorzy:
Ahangar, H. Abdollahzadeh
Amjadi, J.
Chellali, M.
Nazari-Moghaddam, S.
Sheikholeslami, S.M.
Powiązania:
https://bibliotekanauki.pl/articles/32083855.pdf
Data publikacji:
2021-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
2-rainbow dominating function
2-rainbow domination number
total 2-rainbow dominating function
total 2-rainbow domination number
Opis:
A 2-rainbow dominating function (2RDF) of a graph $G = (V(G), E(G))$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set {1, 2} such that for every vertex $v ∈ V(G)$ with $f(v) = ∅$ the condition \(\bigcup_{u∈N(v)}f(u) = \{1, 2\}\) is fulfilled, where $N(v)$ is the open neighborhood of $v$. A total 2-rainbow dominating function $f$ of a graph with no isolated vertices is a 2RDF with the additional condition that the subgraph of $G$ induced by $\{v ∈ V (G) | f(v) ≠∅\}$ has no isolated vertex. The total 2-rainbow domination number, $\gamma_{tr2}(G)$, is the minimum weight of a total 2-rainbow dominating function of $G$. In this paper, we establish some sharp upper and lower bounds on the total 2-rainbow domination number of a tree. Moreover, we show that the decision problem associated with $\gamma_{tr2}(G)$ is NP-complete for bipartite and chordal graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 2; 345-364
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Total Roman Reinforcement in Graphs
Autorzy:
Ahangar, H. Abdollahzadeh
Amjadi, J.
Chellali, M.
Nazari-Moghaddam, S.
Sheikholeslami, S.M.
Powiązania:
https://bibliotekanauki.pl/articles/31343238.pdf
Data publikacji:
2019-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
total Roman domination number
total Roman reinforcement number
Opis:
A total Roman dominating function on a graph G is a labeling f : V (G) → {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2 and the subgraph of G induced by the set of all vertices of positive weight has no isolated vertex. The minimum weight of a total Roman dominating function on a graph G is called the total Roman domination number of G. The total Roman reinforcement number rtR(G) of a graph G is the minimum number of edges that must be added to G in order to decrease the total Roman domination number. In this paper, we investigate the proper- ties of total Roman reinforcement number in graphs, and we present some sharp bounds for rtR(G). Moreover, we show that the decision problem for total Roman reinforcement is NP-hard for bipartite graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 4; 787-803
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Total Roman {2}-Dominating Functions in Graphs
Autorzy:
Ahangar, H. Abdollahzadeh
Chellali, M.
Sheikholeslami, S.M.
Valenzuela-Tripodoro, J.C.
Powiązania:
https://bibliotekanauki.pl/articles/32304142.pdf
Data publikacji:
2022-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Roman domination
Roman {2}-domination
total Roman {2}-domination
Opis:
A Roman {2}-dominating function (R2F) is a function f : V → {0, 1, 2} with the property that for every vertex v ∈ V with f(v) = 0 there is a neighbor u of v with f(u) = 2, or there are two neighbors x, y of v with f(x) = f(y) = 1. A total Roman {2}-dominating function (TR2DF) is an R2F f such that the set of vertices with f(v) > 0 induce a subgraph with no isolated vertices. The weight of a TR2DF is the sum of its function values over all vertices, and the minimum weight of a TR2DF of G is the total Roman {2}-domination number γtR2(G). In this paper, we initiate the study of total Roman {2}-dominating functions, where properties are established. Moreover, we present various bounds on the total Roman {2}-domination number. We also show that the decision problem associated with γtR2(G) is possible to compute this parameter in linear time for bounded clique-width graphs (including trees).
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 3; 937-958
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Cubic Graphs with Total Domatic Number at Least Two
Autorzy:
Akbari, Saieed
Motiei, Mohammad
Mozaffari, Sahand
Yazdanbod, Sina
Powiązania:
https://bibliotekanauki.pl/articles/31342441.pdf
Data publikacji:
2018-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
total domination
total domatic number
coupon coloring
Opis:
Let G be a graph with no isolated vertex. A total dominating set of G is a set S of vertices of G such that every vertex is adjacent to at least one vertex in S. The total domatic number of a graph is the maximum number of total dominating sets which partition the vertex set of G. In this paper we provide a criterion under which a cubic graph has total domatic number at least two.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 1; 75-82
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Note on Path Domination
Autorzy:
Alcón, Liliana
Powiązania:
https://bibliotekanauki.pl/articles/31340460.pdf
Data publikacji:
2016-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination
paths
geodesics
chordal graphs
interval graphs
Opis:
We study domination between different types of walks connecting two non-adjacent vertices u and v of a graph (shortest paths, induced paths, paths, tolled walks). We succeeded in characterizing those graphs in which every uv-walk of one particular kind dominates every uv-walk of other specific kind. We thereby obtained new characterizations of standard graph classes like chordal, interval and superfragile graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 4; 1021-1034
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Independent [1, 2]-Sets in Trees
Autorzy:
Aleid, Sahar A.
Cáceres, José
Puertas, María Luz
Powiązania:
https://bibliotekanauki.pl/articles/31342284.pdf
Data publikacji:
2018-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination
independence
spanning trees
excellent trees
Opis:
An [1, k]-set S in a graph G is a dominating set such that every vertex not in S has at most k neighbors in it. If the additional requirement that the set must be independent is added, the existence of such sets is not guaranteed in every graph. In this paper we solve some problems previously posed by other authors about independent [1, 2]-sets. We provide a necessary condition for a graph to have an independent [1, 2]-set, in terms of spanning trees, and we prove that this condition is also sufficient for cactus graphs. We follow the concept of excellent tree and characterize the family of trees such that any vertex belongs to some independent [1, 2]-set. Finally, we describe a linear algorithm to decide whether a tree has an independent [1, 2]-set. This algorithm can be easily modified to obtain the cardinality of a smallest independent [1, 2]-set of a tree.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 3; 645-660
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:
Various Bounds for Liar’s Domination Number
Autorzy:
Alimadadi, Abdollah
Mojdeh, Doost Ali
Rad, Nader Jafari
Powiązania:
https://bibliotekanauki.pl/articles/31340859.pdf
Data publikacji:
2016-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
liar’s domination
diameter
regular graph
Nordhaus-Gaddum
Opis:
Let $ G = (V,E) $ be a graph. A set $ S \subseteq V $ is a dominating set if \( \bigcup_{v \in S} N[v] = V \), where $ N[v] $ is the closed neighborhood of $ v $. Let $ L \subseteq V $ be a dominating set, and let $v$ be a designated vertex in $V$ (an intruder vertex). Each vertex in $ L \cap N[v] $ can report that $v$ is the location of the intruder, but (at most) one $ x \in L \cap N[v] $ can report any $ w \in N[x] $ as the intruder location or $ x $ can indicate that there is no intruder in $ N[x] $. A dominating set $L$ is called a liar’s dominating set if every $ v \in V (G) $ can be correctly identified as an intruder location under these restrictions. The minimum cardinality of a liar’s dominating set is called the liar’s domination number, and is denoted by $ \gamma_{LR} (G) $. In this paper, we present sharp bounds for the liar’s domination number in terms of the diameter, the girth and clique covering number of a graph. We present two Nordhaus-Gaddum type relations for $ \gamma_{LR} (G) $, and study liar’s dominating set sensitivity versus edge-connectivity. We also present various bounds for the liar’s domination component number, that is, the maximum number of components over all minimum liar’s dominating sets.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 3; 629-641
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Graph Operations and Neighborhood Polynomials
Autorzy:
Alipour, Maryam
Tittmann, Peter
Powiązania:
https://bibliotekanauki.pl/articles/32083862.pdf
Data publikacji:
2021-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
neighborhood complex
neighborhood polynomial
domination polynomial
graph operations
graph degeneracy
Opis:
The neighborhood polynomial of graph G is the generating function for the number of vertex subsets of G of which the vertices have a common neighbor in G. In this paper, we investigate the behavior of this polynomial under several graph operations. Specifically, we provide an explicit formula for the neighborhood polynomial of the graph obtained from a given graph G by vertex attachment. We use this result to propose a recursive algorithm for the calculation of the neighborhood polynomial. Finally, we prove that the neighborhood polynomial can be found in polynomial-time in the class of k-degenerate graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 3; 697-711
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
(C3, C4, C5, C7)-Free Almost Well-Dominated Graphs
Autorzy:
Alizadeh, Hadi
Gözüpek, Didem
Ekinci, Gülnaz Boruzanlı
Powiązania:
https://bibliotekanauki.pl/articles/32387984.pdf
Data publikacji:
2022-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
well-dominated graphs
almost well-dominated graphs
domination gap
Opis:
The domination gap of a graph G is defined as the di erence between the maximum and minimum cardinalities of a minimal dominating set in G. The term well-dominated graphs referring to the graphs with domination gap zero, was first introduced by Finbow et al. [Well-dominated graphs: A collection of well-covered ones, Ars Combin. 25 (1988) 5–10]. In this paper, we focus on the graphs with domination gap one which we term almost well-dominated graphs. While the results by Finbow et al. have implications for almost well-dominated graphs with girth at least 8, we extend these results to (C3, C4, C5, C7)-free almost well-dominated graphs by giving a complete structural characterization for such graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 4; 1099-1117
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Relating 2-Rainbow Domination To Roman Domination
Autorzy:
Alvarado, José D.
Dantas, Simone
Rautenbach, Dieter
Powiązania:
https://bibliotekanauki.pl/articles/31341598.pdf
Data publikacji:
2017-11-27
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
2-rainbow domination
Roman domination
Opis:
For a graph $G$, let $ \gamma_R (G)$ and $ \gamma_{r2} (G) $ denote the Roman domination number of $G$ and the 2-rainbow domination number of $G$, respectively. It is known that $ \gamma_{r2} (G) \le \gamma_R(G) \le 3/2 \gamma_{r2} (G) $. Fujita and Furuya [Difference between 2-rainbow domination and Roman domination in graphs, Discrete Appl. Math. 161 (2013) 806-812] present some kind of characterization of the graphs $G$ for which $ \gamma_R (G) − \gamma_{r2} (G) = k $ for some integer $k$. Unfortunately, their result does not lead to an algorithm that allows to recognize these graphs efficiently. We show that for every fixed non-negative integer $k$, the recognition of the connected $ K_4$-free graphs $G$ with $ \gamma_R (G) − \gamma_{r2} (G) = k $ is NP-hard, which implies that there is most likely no good characterization of these graphs. We characterize the graphs $ G $ such that $ \gamma_{r2} (H) = \gamma_R (H) $ for every induced subgraph $ H $ of $ G $, and collect several properties of the graphs $ G $ with $ \gamma_R (G) = 3/2 \gamma_{r2} (G) $.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 4; 953-961
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On The Total Roman Domination in Trees
Autorzy:
Amjadi, Jafar
Sheikholeslami, Seyed Mahmoud
Soroudi, Marzieh
Powiązania:
https://bibliotekanauki.pl/articles/31343413.pdf
Data publikacji:
2019-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
total Roman dominating function
total Roman domination number
trees
Opis:
A total Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the following conditions: (i) every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2 and (ii) the subgraph of G induced by the set of all vertices of positive weight has no isolated vertex. The weight of a total Roman dominating function f is the value f(V (G)) = Σu∈V(G) f(u). The total Roman domination number γtR(G) is the minimum weight of a total Roman dominating function of G. Ahangar et al. in [H.A. Ahangar, M.A. Henning, V. Samodivkin and I.G. Yero, Total Roman domination in graphs, Appl. Anal. Discrete Math. 10 (2016) 501–517] recently showed that for any graph G without isolated vertices, 2γ(G) ≤ γtR(G) ≤ 3γ(G), where γ(G) is the domination number of G, and they raised the problem of characterizing the graphs G achieving these upper and lower bounds. In this paper, we provide a constructive characterization of these trees.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 2; 519-532
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 327

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