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Wyświetlanie 1-15 z 175
Tytuł:
Digraphs with isomorphic underlying and domination graphs: connected $UG^c(d)$
Autorzy:
Factor, Kim
Langley, Larry
Powiązania:
https://bibliotekanauki.pl/articles/743665.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination graph
domination
graph isomorphism
underlying graph
Opis:
The domination graph of a directed graph has an edge between vertices x and y provided either (x,z) or (y,z) is an arc for every vertex z distinct from x and y. We consider directed graphs D for which the domination graph of D is isomorphic to the underlying graph of D. We demonstrate that the complement of the underlying graph must have k connected components isomorphic to complete graphs, paths, or cycles. A complete characterization of directed graphs where k = 1 is presented.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 1; 51-67
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
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:
Effect of edge-subdivision on vertex-domination in a graph
Autorzy:
Bhattacharya, Amitava
Vijayakumar, Gurusamy
Powiązania:
https://bibliotekanauki.pl/articles/743368.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination number
subdivision number
matching
Opis:
Let G be a graph with Δ(G) > 1. It can be shown that the domination number of the graph obtained from G by subdividing every edge exactly once is more than that of G. So, let ξ(G) be the least number of edges such that subdividing each of these edges exactly once results in a graph whose domination number is more than that of G. The parameter ξ(G) is called the subdivision number of G. This notion has been introduced by S. Arumugam and S. Velammal. They have conjectured that for any graph G with Δ(G) > 1, ξ(G) ≤ 3. We show that the conjecture is false and construct for any positive integer n ≥ 3, a graph G of order n with ξ(G) > [1/3]log₂ n. The main results of this paper are the following: (i) For any connected graph G with at least three vertices, ξ(G) ≤ γ(G)+1 where γ(G) is the domination number of G. (ii) If G is a connected graph of sufficiently large order n, then ξ(G) ≤ 4√n ln n+5
Źródło:
Discussiones Mathematicae Graph Theory; 2002, 22, 2; 335-347
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Domination Parameters of a Graph and its Complement
Autorzy:
Desormeaux, Wyatt J.
Haynes, Teresa W.
Henning, Michael A.
Powiązania:
https://bibliotekanauki.pl/articles/31342430.pdf
Data publikacji:
2018-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination
complement
total domination
connected domination
clique domination
restrained domination
Opis:
A dominating set in a graph G is a set S of vertices such that every vertex in V (G) \ S is adjacent to at least one vertex in S, and the domination number of G is the minimum cardinality of a dominating set of G. Placing constraints on a dominating set yields different domination parameters, including total, connected, restrained, and clique domination numbers. In this paper, we study relationships among domination parameters of a graph and its complement.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 1; 203-215
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
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:
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:
Total Domination Multisubdivision Number of a Graph
Autorzy:
Avella-Alaminos, Diana
Dettlaff, Magda
Lemańska, Magdalena
Zuazua, Rita
Powiązania:
https://bibliotekanauki.pl/articles/31339480.pdf
Data publikacji:
2015-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
(total) domination
(total) domination subdivision number
(total) domination multisubdivision number
trees
Opis:
The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. Similarly we define the total domination multisubdivision number msdγt (G) of a graph G and we show that for any connected graph G of order at least two, msdγt (G) ≤ 3. We show that for trees the total domination multisubdivision number is equal to the known total domination subdivision number. We also determine the total domination multisubdivision number for some classes of graphs and characterize trees T with msdγt (T) = 1.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 2; 315-327
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bounds on the Double Italian Domination Number of a Graph
Autorzy:
Azvin, Farzaneh
Rad, Nader Jafari
Powiązania:
https://bibliotekanauki.pl/articles/32222552.pdf
Data publikacji:
2022-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Italian domination
double Italian domination
probabilistic methods
Opis:
For a graph G, a Roman {3}-dominating function is a function f : V → {0, 1, 2, 3} having the property that for every vertex u ∈ V, if f(u) ∈ {0, 1}, then f(N[u]) ≥ 3. The weight of a Roman {3}-dominating function is the sum w(f) = f(V) = Σv∈V f(v), and the minimum weight of a Roman {3}-dominating function is the Roman {3}-domination number, denoted by γ{R3}(G). In this paper, we present a sharp lower bound for the double Italian domination number of a graph, and improve previous bounds given in [D.A. Mojdeh and L. Volkmann, Roman {3}-domination (double Italian domination), Discrete Appl. Math. 283 (2022) 555–564]. We also present a probabilistic upper bound for a generalized version of double Italian domination number of a graph, and show that the given bound is asymptotically best possible.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 4; 1129-1137
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The independent domination number of a random graph
Autorzy:
Clark, Lane
Johnson, Darin
Powiązania:
https://bibliotekanauki.pl/articles/743841.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
random graph
two-point concentration
independent domination
Opis:
We prove a two-point concentration for the independent domination number of the random graph $G_{n,p}$ provided p²ln(n) ≥ 64ln((lnn)/p).
Źródło:
Discussiones Mathematicae Graph Theory; 2011, 31, 1; 129-142
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Graphs without induced P₅ and C₅
Autorzy:
Bacsó, Gabor
Tuza, Zsolt
Powiązania:
https://bibliotekanauki.pl/articles/744580.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph domination
connected domination
complete subgraph
forbidden induced subgraph
characterization
Opis:
Zverovich [Discuss. Math. Graph Theory 23 (2003), 159-162.] has proved that the domination number and connected domination number are equal on all connected graphs without induced P₅ and C₅. Here we show (with an independent proof) that the following stronger result is also valid: Every P₅-free and C₅-free connected graph contains a minimum-size dominating set that induces a complete subgraph.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 3; 503-507
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Domination parameters of a graph with deleted special subset of edges
Autorzy:
Kwaśnik, Maria
Zwierzchowski, Maciej
Powiązania:
https://bibliotekanauki.pl/articles/743487.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination parameters
edge deleted graphs
Opis:
This paper contains a number of estimations of the split domination number and the maximal domination number of a graph with a deleted subset of edges which induces a complete subgraph Kₚ. We discuss noncomplete graphs having or not having hanging vertices. In particular, for p = 2 the edge deleted graphs are considered. The motivation of these problems comes from [2] and [6], where the authors, among other things, gave the lower and upper bounds on irredundance, independence and domination numbers of an edge deleted graph.
Źródło:
Discussiones Mathematicae Graph Theory; 2001, 21, 2; 229-238
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nordhaus-Gaddum results for weakly convex domination number of a graph
Autorzy:
Lemańska, Magdalena
Powiązania:
https://bibliotekanauki.pl/articles/744253.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
weakly convex domination number
Nordhaus-Gaddum results
Opis:
Nordhaus-Gaddum results for weakly convex domination number of a graph G are studied.
Źródło:
Discussiones Mathematicae Graph Theory; 2010, 30, 2; 257-263
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Gallai-type equality for the total domination number of a graph
Autorzy:
Zhou, Sanming
Powiązania:
https://bibliotekanauki.pl/articles/744259.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination number
total domination number
Gallai equality
Opis:
We prove the following Gallai-type equality
γₜ(G) + εₜ(G) = p
for any graph G with no isolated vertex, where p is the number of vertices of G, γₜ(G) is the total domination number of G, and εₜ(G) is the maximum integer s such that there exists a spanning forest F with s the number of pendant edges of F minus the number of star components of F.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 3; 539-543
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Changing and Unchanging of the Domination Number of a Graph: Path Addition Numbers
Autorzy:
Samodivkin, Vladimir
Powiązania:
https://bibliotekanauki.pl/articles/32083856.pdf
Data publikacji:
2021-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination number
path addition
Opis:
Given a graph $G=(V, E)$ and two its distinct vertices $u$ and $v$, the $(u, v)$-$P_k$-addition graph of $G$ is the graph $G_{u,v,k−2}$ obtained from disjoint union of $G$ and a path $P_k : x_0, x_1,...,x_{k−1}, k ≥ 2$, by identifying the vertices $u$ and $x_0$, and identifying the vertices $v$ and $x_{k−1}$. We prove that $\gamma(G) − 1 ≤ \gamma(G_{u,v,k})$ for all $k ≥ 1$, and $\gamma(G_{u,v,k})>\gamma(G)$ when $k ≥ 5$. We also provide necessary and sufficient conditions for the equality $\gamma(G_{u,v,k})=\gamma(G)$ to be valid for each pair $u, v ∈ V(G)$. In addition, we establish sharp upper and lower bounds for the minimum, respectively maximum, $k$ in a graph $G$ over all pairs of vertices $u$ and $v$ in $G$ such that the $(u, v)$-$P_k$-addition graph of $G$ has a larger domination number than $G$, which we consider separately for adjacent and non-adjacent pairs of vertices.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 2; 365-379
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An application of the selected graph theory domination concepts to transportation networks modelling
Autorzy:
Guze, S.
Powiązania:
https://bibliotekanauki.pl/articles/135168.pdf
Data publikacji:
2017
Wydawca:
Akademia Morska w Szczecinie. Wydawnictwo AMSz
Tematy:
domination
edge-subdivision
connected bondage number
bondage-connected number
transportation network
modelling
Opis:
One of the possibilities when modelling a transport network is to use a graph with vertices and edges. They represent the nodes and arcs of such a network respectively. There are dozens of parameters or characteristics that we can describe in graphs, including the different types of domination number and the problems related to it. The main aim of this paper has been to show the possibilities of the application of the selected domination-oriented concepts to modelling and improving the transportation and/or logistics networks. Firstly, the basic description of domination in graph theory has been introduced. The edge-subdivision and bondage number notations and their implementations to the transportation network description and modelling were then proposed. Furthermore, the possible usage of distinguishing concepts in an exemplary academic transportation network has been shown. Finally, the conclusions and future directions of the work have been presented.
Źródło:
Zeszyty Naukowe Akademii Morskiej w Szczecinie; 2017, 52 (124); 97-102
1733-8670
2392-0378
Pojawia się w:
Zeszyty Naukowe Akademii Morskiej w Szczecinie
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 175

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