Temat: connected - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Perfect connected-dominant graphs
Autorzy:: Zverovich, Igor
Tematy:: Connected domination
perfect connected-dominant graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743393.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: The connected forcing connected vertex detour number of a graph
Autorzy:: Santhakumaran, A.
Titus, P.
Tematy:: vertex detour number
connected vertex detour number
upper connected vertex detour number
forcing connected vertex detour number
connected forcing connected vertex detour number; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743939.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: A New Proof that 4-Connected Planar Graphs are Hamiltonian-Connected
Autorzy:: Lu, Xiaoyun
West, Douglas B.
Tematy:: 4-connected planar graph
Hamiltonian-connected
Tutte-path; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31340879.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Weakly connected domination subdivision numbers
Autorzy:: Raczek, Joanna
Tematy:: weakly connected domination number
weakly connected domination subdivision number; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743529.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Domination numbers in graphs with removed edge or set of edges
Autorzy:: Lemańska, Magdalena
Tematy:: connected domination number
weakly connected domination number
edge removal; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/744295.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 6.

Tytuł:: Connected Domination Critical Graphs with Cut Vertices
Autorzy:: Kaemawichanurat, Pawaton
Ananchuen, Nawarat
Tematy:: connected domination
critical; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31348137.pdf Link otwiera się w nowym oknie
Opis:: A graph G is said to be k-γ_c-critical if the connected domination number of G, γ_c(G), is k and γ_c(G + uv) < k for any pair of non-adjacent vertices u and v of G. Let G be a k-γ_c-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-γ_c-critical graph satisfies ζ (G) ≤ k − 2. In this paper, we generalize that every k-γ_c-critical graph satisfies ζ (G) ≤ k − 2 for all k ≥ 5. We also characterize all k-γ_c-critical graphs when ζ(G) is achieving the upper bound.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 7.

Tytuł:: Edge-Connectivity and Edges of Even Factors of Graphs
Autorzy:: Haghparast, Nastaran
Kiani, Dariush
Tematy:: 3-edge-connected graph
2-edge-connected graph
even factor
component; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31343450.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 8.

Tytuł:: Total connected domination game
Autorzy:: Bujtás, Csilla
Henning, Michael A.
Iršič, Vesna
Klavžar, Sandi
Tematy:: connected domination game
total connected domination game
graph product
tree; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/2050904.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 9.

Tytuł:: Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number
Autorzy:: Volkmann, Lutz
Tematy:: edge-connectivity
clique number
maximally edge-connected graphs
super-edge-connected graphs; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31343389.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 10.

Tytuł:: A Note on Cycles in Locally Hamiltonian and Locally Hamilton-Connected Graphs
Autorzy:: Tang, Long
Vumar, Elkin
Tematy:: locally connected
locally Hamiltonian
locally Hamilton-connected
fully cycle extendability
weakly pancyclicity; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/32032199.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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