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Tytuł:
Perfect connected-dominant graphs
Autorzy:
Zverovich, Igor
Powiązania:
https://bibliotekanauki.pl/articles/743393.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Connected domination
perfect connected-dominant graph
Opis:
If D is a dominating set and the induced subgraph G(D) is connected, then D is a connected dominating set. The minimum size of a connected dominating set in G is called connected domination number $γ_c(G)$ of G. A graph G is called a perfect connected-dominant graph if $γ(H) = γ_c(H)$ for each connected induced subgraph H of G.We prove that a graph is a perfect connected-dominant graph if and only if it contains no induced path P₅ and induced cycle C₅.
Źródło:
Discussiones Mathematicae Graph Theory; 2003, 23, 1; 159-162
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The connected forcing connected vertex detour number of a graph
Autorzy:
Santhakumaran, A.
Titus, P.
Powiązania:
https://bibliotekanauki.pl/articles/743939.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
vertex detour number
connected vertex detour number
upper connected vertex detour number
forcing connected vertex detour number
connected forcing connected vertex detour number
Opis:
For any vertex x in a connected graph G of order p ≥ 2, a set S of vertices of V is an x-detour set of G if each vertex v in G lies on an x-y detour for some element y in S. A connected x-detour set of G is an x-detour set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected x-detour set of G is the connected x-detour number of G and is denoted by cdₓ(G). For a minimum connected x-detour set Sₓ of G, a subset T ⊆ Sₓ is called a connected x-forcing subset for Sₓ if the induced subgraph G[T] is connected and Sₓ is the unique minimum connected x-detour set containing T. A connected x-forcing subset for Sₓ of minimum cardinality is a minimum connected x-forcing subset of Sₓ. The connected forcing connected x-detour number of Sₓ, denoted by $cf_{cdx}(Sₓ)$, is the cardinality of a minimum connected x-forcing subset for Sₓ. The connected forcing connected x-detour number of G is $cf_{cdx}(G) = mincf_{cdx}(Sₓ)$, where the minimum is taken over all minimum connected x-detour sets Sₓ in G. Certain general properties satisfied by connected x-forcing sets are studied. The connected forcing connected vertex detour numbers of some standard graphs are determined. It is shown that for positive integers a, b, c and d with 2 ≤ a < b ≤ c ≤ d, there exists a connected graph G such that the forcing connected x-detour number is a, connected forcing connected x-detour number is b, connected x-detour number is c and upper connected x-detour number is d, where x is a vertex of G.
Źródło:
Discussiones Mathematicae Graph Theory; 2011, 31, 3; 461-473
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A New Proof that 4-Connected Planar Graphs are Hamiltonian-Connected
Autorzy:
Lu, Xiaoyun
West, Douglas B.
Powiązania:
https://bibliotekanauki.pl/articles/31340879.pdf
Data publikacji:
2016-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
4-connected planar graph
Hamiltonian-connected
Tutte-path
Opis:
We prove a theorem guaranteeing special paths of faces in 2-connected plane graphs. As a corollary, we obtain a new proof of Thomassen’s theorem that every 4-connected planar graph is Hamiltonian-connected.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 3; 555-564
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weakly connected domination subdivision numbers
Autorzy:
Raczek, Joanna
Powiązania:
https://bibliotekanauki.pl/articles/743529.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
weakly connected domination number
weakly connected domination subdivision number
Opis:
A set D of vertices in a graph G = (V,E) is a weakly connected dominating set of G if D is dominating in G and the subgraph weakly induced by D is connected. The weakly connected domination number of G is the minimum cardinality of a weakly connected dominating set of G. The weakly connected domination subdivision number of a connected graph G is the minimum number of edges that must be subdivided (where each egde can be subdivided at most once) in order to increase the weakly connected domination number. We study the weakly connected domination subdivision numbers of some families of graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2008, 28, 1; 109-119
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Connected Domination Critical Graphs with Cut Vertices
Autorzy:
Kaemawichanurat, Pawaton
Ananchuen, Nawarat
Powiązania:
https://bibliotekanauki.pl/articles/31348137.pdf
Data publikacji:
2020-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
connected domination
critical
Opis:
A graph G is said to be k-γc-critical if the connected domination number of G, γc(G), is k and γc(G + uv) < k for any pair of non-adjacent vertices u and v of G. Let G be a k-γc-critical graph and ζ (G) the number of cut vertices of G. It was proved, in [1, 6], that, for 3 ≤ k ≤ 4, every k-γc-critical graph satisfies ζ (G) ≤ k − 2. In this paper, we generalize that every k-γc-critical graph satisfies ζ (G) ≤ k − 2 for all k ≥ 5. We also characterize all k-γc-critical graphs when ζ(G) is achieving the upper bound.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 4; 1035-1055
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Domination numbers in graphs with removed edge or set of edges
Autorzy:
Lemańska, Magdalena
Powiązania:
https://bibliotekanauki.pl/articles/744295.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
connected domination number
weakly connected domination number
edge removal
Opis:
It is known that the removal of an edge from a graph G cannot decrease a domination number γ(G) and can increase it by at most one. Thus we can write that γ(G) ≤ γ(G-e) ≤ γ(G)+1 when an arbitrary edge e is removed. Here we present similar inequalities for the weakly connected domination number $γ_w$ and the connected domination number $γ_c$, i.e., we show that $γ_w(G) ≤ γ_w(G-e) ≤ γ_w(G)+1$ and $γ_c(G) ≤ γ_c(G-e) ≤ γ_c(G) + 2$ if G and G-e are connected. Additionally we show that $γ_w(G) ≤ γ_w(G-Eₚ) ≤ γ_w(G) + p - 1$ and $γ_c(G) ≤ γ_c(G -Eₚ) ≤ γ_c(G) + 2p - 2$ if G and G - Eₚ are connected and Eₚ = E(Hₚ) where Hₚ of order p is a connected subgraph of G.
Źródło:
Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 51-56
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
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:
Edge-Connectivity and Edges of Even Factors of Graphs
Autorzy:
Haghparast, Nastaran
Kiani, Dariush
Powiązania:
https://bibliotekanauki.pl/articles/31343450.pdf
Data publikacji:
2019-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
3-edge-connected graph
2-edge-connected graph
even factor
component
Opis:
An even factor of a graph is a spanning subgraph in which each vertex has a positive even degree. Jackson and Yoshimoto showed that if G is a 3-edge-connected graph with |G| ≥ 5 and v is a vertex with degree 3, then G has an even factor F containing two given edges incident with v in which each component has order at least 5. We prove that this theorem is satisfied for each pair of adjacent edges. Also, we show that each 3-edge-connected graph has an even factor F containing two given edges e and f such that every component containing neither e nor f has order at least 5. But we construct infinitely many 3-edge-connected graphs that do not have an even factor F containing two arbitrary prescribed edges in which each component has order at least 5.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 2; 357-364
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Improved Sufficient Conditions for Hamiltonian Properties
Autorzy:
Bode, Jens-P.
Fricke, Anika
Kemnitz, Arnfried
Powiązania:
https://bibliotekanauki.pl/articles/31339476.pdf
Data publikacji:
2015-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Hamiltonian
traceable
Hamiltonian-connected
Opis:
In 1980 Bondy [2] proved that a (k+s)-connected graph of order n ≥ 3 is traceable (s = −1) or Hamiltonian (s = 0) or Hamiltonian-connected (s = 1) if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1)(n+s−1)+1)/2. It is shown in [1] that one can allow exceptional (k+1)-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity condition.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 2; 329-334
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Connected speech in EFL pedagogy
Autorzy:
Jednaszewski, Piotr
Powiązania:
https://bibliotekanauki.pl/articles/40407740.pdf
Data publikacji:
2022
Wydawca:
Uniwersytet Kardynała Stefana Wyszyńskiego w Warszawie
Tematy:
teaching connected speech
teaching phonology
connected speech activities
teaching EFL/ELT
Źródło:
Forum Pedagogiczne; 2022, 12, 1; 459-472
2083-6325
Pojawia się w:
Forum Pedagogiczne
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number
Autorzy:
Volkmann, Lutz
Powiązania:
https://bibliotekanauki.pl/articles/31343389.pdf
Data publikacji:
2019-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge-connectivity
clique number
maximally edge-connected graphs
super-edge-connected graphs
Opis:
Let G be a connected graph with minimum degree δ and edge-connectivity λ. A graph is maximally edge-connected if λ = δ, and it is super-edgeconnected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. The clique number ω(G) of a graph G is the maximum cardinality of a complete subgraph of G. In this paper, we show that a connected graph G with clique number ω(G) ≤ r is maximally edge-connected or super-edge-connected if the number of edges is large enough. These are generalizations of corresponding results for triangle-free graphs by Volkmann and Hong in 2017.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 2; 567-573
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Note on Cycles in Locally Hamiltonian and Locally Hamilton-Connected Graphs
Autorzy:
Tang, Long
Vumar, Elkin
Powiązania:
https://bibliotekanauki.pl/articles/32032199.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
locally connected
locally Hamiltonian
locally Hamilton-connected
fully cycle extendability
weakly pancyclicity
Opis:
Let \(\mathcal{P}\) be a property of a graph. A graph G is said to be locally \(\mathcal{P}\), if the subgraph induced by the open neighbourhood of every vertex in G has property \(\mathcal{P}\). Ryjáček conjectures that every connected, locally connected graph is weakly pancyclic. Motivated by the above conjecture, van Aardt et al. [S.A.van Aardt, M. Frick, O.R. Oellermann and J.P.de Wet, Global cycle properties in locally connected, locally traceable and locally Hamiltonian graphs, Discrete Appl. Math. 205 (2016) 171–179] investigated the global cycle structures in connected, locally traceable/Hamiltonian graphs. Among other results, they proved that a connected, locally Hamiltonian graph G with maximum degree at least |V (G)| − 5 is weakly pancyclic. In this note, we improve this result by showing that such a graph with maximum degree at least |V (G)|−6 is weakly pancyclic. Furthermore, we show that a connected, locally Hamilton-connected graph with maximum degree at most 7 is fully cycle extendable.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 77-84
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
Tytuł:
Dimensionsgrad for locally connected Polish spaces
Autorzy:
Fedorchuk, Vitaly
van Mill, Jan
Powiązania:
https://bibliotekanauki.pl/articles/1205128.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Dimensionsgrad
dimension
locally connected space
Opis:
It is shown that for every n ≥ 2 there exists an n-dimensional locally connected Polish space with Dimensionsgrad 1.
Źródło:
Fundamenta Mathematicae; 2000, 163, 1; 77-82
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Proper Diameter of a Graph
Autorzy:
Coll, Vincent
Hook, Jonelle
Magnant, Colton
McCready, Karen
Ryan, Kathleen
Powiązania:
https://bibliotekanauki.pl/articles/32062335.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
diameter
properly connected
proper diameter
Opis:
A proper edge-coloring of a graph is a coloring in which adjacent edges receive distinct colors. A path is properly colored if consecutive edges have distinct colors, and an edge-colored graph is properly connected if there exists a properly colored path between every pair of vertices. In such a graph, we introduce the notion of the graph’s proper diameter—which is a function of both the graph and the coloring—and define it to be the maximum length of a shortest properly colored path between any two vertices in the graph. We consider various families of graphs to find bounds on the gap between the diameter and possible proper diameters, paying singular attention to 2-colorings.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 107-125
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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