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Wyświetlanie 1-15 z 46
Tytuł:
On minimum intersections of certain secondary dominating sets in graphs
Autorzy:
Kosiorowska, Anna
Michalski, Adrian
Włoch, Iwona
Powiązania:
https://bibliotekanauki.pl/articles/29519420.pdf
Data publikacji:
2023
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
dominating set
2-dominating set
(1, 2)-dominating set
proper (1, 2)-dominating set
domination number
(1,2)-intersection index
Opis:
In this paper we consider secondary dominating sets, also named as (1,k)-dominating sets, introduced by Hedetniemi et al. in 2008. In particular, we study intersections of the (1, 1)-dominating sets and proper (1, 2)-dominating sets. We introduce (1,2̅)-intersection index as the minimum possible cardinality of such intersection and determine its value for some classes of graphs.
Źródło:
Opuscula Mathematica; 2023, 43, 6; 813-827
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Mf-Edge Colorings of Graphs
Autorzy:
Ivančo, Jaroslav
Onderko, Alfréd
Powiązania:
https://bibliotekanauki.pl/articles/32222570.pdf
Data publikacji:
2022-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge coloring
anti-Ramsey number
dominating set
Opis:
An edge coloring φ of a graph G is called an Mf-edge coloring if |φ(v)| ≤ f(v) for every vertex v of G, where φ(v) is the set of colors of edges incident with v and f is a function which assigns a positive integer f(v) to each vertex v. Let Kf (G) denote the maximum number of colors used in an Mf-edge coloring of G. In this paper we establish some bounds on Kf(G), present some graphs achieving the bounds and determine exact values of Kf(G) for some special classes of graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 4; 1075-1088
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
γ-paired dominating graphs of cycles
Autorzy:
Eakawinrujee, Pannawat
Trakultraipruk, Nantapath
Powiązania:
https://bibliotekanauki.pl/articles/2048671.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
paired dominating graph
paired dominating set
paired-domination number
Opis:
A paired dominating set of a graph G is a dominating set whose induced subgraph contains a perfect matching. The paired domination number, denoted by γpr(G), is the minimum cardinality of a paired dominating set of G. A γpr(G)-set is a paired dominating set of cardinality γpr(G). The γ-paired dominating graph of G, denoted by PDγ(G), as the graph whose vertices are γpr(G)-sets. Two γpr(G)-sets D1 and D2 are adjacent in PDγ(G) if there exists a vertex u ∈ D1 and a vertex v /∈ D1 such that D2 = (D1 \ {u}) ∪ {v}. In this paper, we present the γ-paired dominating graphs of cycles.
Źródło:
Opuscula Mathematica; 2022, 42, 1; 31-54
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dominating Vertex Covers: The Vertex-Edge Domination Problem
Autorzy:
Klostermeyer, William F.
Messinger, Margaret-Ellen
Yeo, Anders
Powiązania:
https://bibliotekanauki.pl/articles/32083812.pdf
Data publikacji:
2021-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cubic graph
dominating set
vertex cover
vertex-edge dominating set
Opis:
The vertex-edge domination number of a graph, γve(G), is defined to be the cardinality of a smallest set D such that there exists a vertex cover C of G such that each vertex in C is dominated by a vertex in D. This is motivated by the problem of determining how many guards are needed in a graph so that a searchlight can be shone down each edge by a guard either incident to that edge or at most distance one from a vertex incident to the edge. Our main result is that for any cubic graph G with n vertices, γve(G) ≤ 9n/26. We also show that it is NP-hard to decide if γve(G) = γ(G) for bipartite graph G.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 1; 123-132
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:
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 γe(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) = γe(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
Tytuł:
Bounds on the Locating-Total Domination Number in Trees
Autorzy:
Wang, Kun
Ning, Wenjie
Lu, Mei
Powiązania:
https://bibliotekanauki.pl/articles/31867549.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
tree
total dominating set
locating-total dominating set
locating-total domination number
Opis:
Given a graph $G = (V, E)$ with no isolated vertex, a subset $S$ of $V$ is called a total dominating set of $G$ if every vertex in $V$ has a neighbor in $S$. A total dominating set $S$ is called a locating-total dominating set if for each pair of distinct vertices $u$ and $v$ in $V \ S, N(u) ∩ S ≠ N(v) ∩ S$. The minimum cardinality of a locating-total dominating set of $G$ is the locating-total domination number, denoted by $γ_t^L(G)$. We show that, for a tree $T$ of order $n ≥ 3$ and diameter $d$, \(\frac{d+1}{2}≤γ_t^L(T)≤n−\frac{d−1}{2}\), and if $T$ has $l$ leaves, $s$ support vertices and $s_1$ strong support vertices, then \(γ_t^L(T)≥max\Big\{\frac{n+l−s+1}{2}−\frac{s+s_1}{4},\frac{2(n+1)+3(l−s)−s_1}{5}\Big\}\). We also characterize the extremal trees achieving these bounds.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 25-34
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Compared Costs of Domination Location-Domination and Identification
Autorzy:
Hudry, Olivier
Lobstein, Antoine
Powiązania:
https://bibliotekanauki.pl/articles/32083840.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph theory
dominating set
locating-dominating code
identifying code
twin-free graph
Opis:
Let G = (V, E) be a finite graph and r ≥ 1 be an integer. For v ∈ V, let Br(v) = {x ∈ V : d(v, x) ≤ r} be the ball of radius r centered at v. A set C ⊆ V is an r-dominating code if for all v ∈ V, we have Br(v) ∩ C ≠ ∅; it is an r-locating-dominating code if for all v ∈ V, we have Br(v) ∩ C ≠ ∅, and for any two distinct non-codewords x ∈ V \ C, y ∈ V \ C, we have Br(x) ∩ C ≠ Br(y) ∩ C; it is an r-identifying code if for all v ∈ V, we have Br(v) ∩ C ≠ ∅, and for any two distinct vertices x ∈ V, y ∈ V, we have Br(x) ∩ C ≠ Br(y) ∩ C. We denote by γr(G) (respectively, ldr(G) and idr(G)) the smallest possible cardinality of an r-dominating code (respectively, an r-locating-dominating code and an r-identifying code). We study how small and how large the three differences idr(G)−ldr(G), idr(G)−γr(G) and ldr(G) − γr(G) can be.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 127-147
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees
Autorzy:
Rad, Nader Jafari
Rahbani, Hadi
Powiązania:
https://bibliotekanauki.pl/articles/31342324.pdf
Data publikacji:
2018-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
locating-dominating set
differentiating-total dominating set
tree
Opis:
A subset $S$ of vertices in a graph $G = (V,E)$ is a dominating set of $G$ if every vertex in $V − S$ has a neighbor in $S$, and is a total dominating set if every vertex in $V$ has a neighbor in $S$. A dominating set $S$ is a locating-dominating set of $G$ if every two vertices $ x, y \in V − S$ satisfy $N(x) \cap S \ne N(y) \cap S$. The locating-domination number $ \gamma_L (G) $ is the minimum cardinality of a locating-dominating set of $G$. A total dominating set $S$ is called a differentiating-total dominating set if for every pair of distinct vertices $u$ and $v$ of $G$, $ N[u] \cap S \ne N[v] \cap S $. The minimum cardinality of a differentiating-total dominating set of $G$ is the differentiating-total domination number of $G$, denoted by $ \gamma_t^D (G) $. We obtain new upper bounds for the locating-domination number, and the differentiating-total domination number in trees. Moreover, we characterize all trees achieving equality for the new bounds.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 2; 455-462
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Making a Dominating Set of a Graph Connected
Autorzy:
Li, Hengzhe
Wu, Baoyindureng
Yang, Weihua
Powiązania:
https://bibliotekanauki.pl/articles/31342251.pdf
Data publikacji:
2018-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
independent set
dominating set
connected dominating set
Opis:
Let $ G = (V,E) $ be a graph and $ S \subseteq V $. We say that $ S $ is a dominating set of $ G $, if each vertex in $ V \backlash S $ has a neighbor in $S$. Moreover, we say that $S$ is a connected (respectively, 2-edge connected or 2-connected) dominating set of $G$ if $ G[S] $ is connected (respectively, 2-edge connected or 2-connected). The domination (respectively, connected domination, or 2-edge connected domination, or 2-connected domination) number of $G$ is the cardinality of a minimum dominating (respectively, connected dominating, or 2-edge connected dominating, or 2-connected dominating) set of $G$, and is denoted $ \gamma (G) $ (respectively $ \gamma_1 (G) $, or $ \gamma_2^′ (G) $, or $ \gamma_2 (G) $). A well-known result of Duchet and Meyniel states that $ \gamma_1 (G) \le 3 \gamma (G) − 2 $ for any connected graph $G$. We show that if $ \gamma (G) \ge 2 $, then $ \gamma_2^′ (G) \ge 5 \gamma (G) − 4 $ when $G$ is a 2-edge connected graph and $ \gamma_2 (G) \le 11 \gamma (G) − 13 $ when $G$ is a 2-connected triangle-free graph.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 4; 947-962
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Note on the Locating-Total Domination in Graphs
Autorzy:
Miller, Mirka
Rajan, R. Sundara
Jayagopal, R.
Rajasingh, Indra
Manuel, Paul
Powiązania:
https://bibliotekanauki.pl/articles/31341658.pdf
Data publikacji:
2017-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
dominating set
total dominating set
locating-dominating set
locating-total dominating set
regular graphs
Opis:
In this paper we obtain a sharp (improved) lower bound on the locating-total domination number of a graph, and show that the decision problem for the locating-total domination is NP-complete.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 3; 745-754
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Distance 2-Domination in Prisms of Graphs
Autorzy:
Hurtado, Ferran
Mora, Mercè
Rivera-Campo, Eduardo
Zuazua, Rita
Powiązania:
https://bibliotekanauki.pl/articles/31341963.pdf
Data publikacji:
2017-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
distance 2 dominating set
prisms of graphs
universal fixer
Opis:
A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ∊ (V (G) − D) and D is at most two. Let γ2(G) denote the size of a smallest distance 2-dominating set of G. For any permutation π of the vertex set of G, the prism of G with respect to π is the graph πG obtained from G and a copy G′ of G by joining u ∊ V(G) with v′ ∊ V(G′) if and only if v′ = π(u). If γ2(πG) = γ2(G) for any permutation π of V(G), then G is called a universal γ2-fixer. In this work we characterize the cycles and paths that are universal γ2-fixers.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 2; 383-397
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Eternal Domination: Criticality and Reachability
Autorzy:
Klostermeyer, William F.
MacGillivray, Gary
Powiązania:
https://bibliotekanauki.pl/articles/31342174.pdf
Data publikacji:
2017-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
dominating set
eternal dominating set
critical graphs
Opis:
We show that for every minimum eternal dominating set, D, of a graph G and every vertex v ∈ D, there is a sequence of attacks at the vertices of G which can be defended in such a way that an eternal dominating set not containing v is reached. The study of the stronger assertion that such a set can be reached after a single attack is defended leads to the study of graphs which are critical in the sense that deleting any vertex reduces the eternal domination number. Examples of these graphs and tight bounds on connectivity, edge-connectivity and diameter are given. It is also shown that there exist graphs in which deletion of any edge increases the eternal domination number, and graphs in which addition of any edge decreases the eternal domination number.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 1; 63-77
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
M2-edge colorings of dense graphs
Autorzy:
Ivanco, J.
Powiązania:
https://bibliotekanauki.pl/articles/254913.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
edge coloring
dominating set
dense graphs
Opis:
An edge coloring φ of a graph G is called an Mi-edge coloring if [formula] every vertex v of G, where φ (v) is the set of colors of edges incident with v. Let K1(G) denote the maximum number of colors used in an Mi-edge coloring of G. In this paper we establish some bounds of K.2(G), present some graphs achieving the bounds and determine exact values of K.2(G) for dense graphs.
Źródło:
Opuscula Mathematica; 2016, 36, 5; 603-612
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Quest for A Characterization of Hom-Properties of Finite Character
Autorzy:
Broere, Izak
Matsoha, Moroli D.V.
Heidema, Johannes
Powiązania:
https://bibliotekanauki.pl/articles/31340894.pdf
Data publikacji:
2016-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
(countable) graph
homomorphism (of graphs)
property of graphs
hom-property
(finitely-)induced-hereditary property
finitely determined property
(weakly) finite character
axiomatizable property
compactness theorems
core
connectedness
chromatic number
clique number
independence number
dominating set
Opis:
A graph property is a set of (countable) graphs. A homomorphism from a graph \( G \) to a graph \( H \) is an edge-preserving map from the vertex set of \( G \) into the vertex set of \( H \); if such a map exists, we write \( G \rightarrow H \). Given any graph \( H \), the hom-property \( \rightarrow H \) is the set of \( H \)-colourable graphs, i.e., the set of all graphs \( G \) satisfying \( G \rightarrow H \). A graph property \( mathcal{P} \) is of finite character if, whenever we have that \( F \in \mathcal{P} \) for every finite induced subgraph \( F \) of a graph \( G \), then we have that \( G \in \mathcal{P} \) too. We explore some of the relationships of the property attribute of being of finite character to other property attributes such as being finitely-induced-hereditary, being finitely determined, and being axiomatizable. We study the hom-properties of finite character, and prove some necessary and some sufficient conditions on \( H \) for \( \rightarrow H \) to be of finite character. A notable (but known) sufficient condition is that \( H \) is a finite graph, and our new model-theoretic proof of this compactness result extends from hom-properties to all axiomatizable properties. In our quest to find an intrinsic characterization of those \( H \) for which \( \rightarrow H \) is of finite character, we find an example of an infinite connected graph with no finite core and chromatic number 3 but with hom-property not of finite character.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 2; 479-500
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 46

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