Temat: dominating cycle - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Vertex-dominating cycles in 2-connected bipartite graphs
Autorzy:: Yamashita, Tomoki
Tematy:: vertex-dominating cycle
dominating cycle
bipartite graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743795.pdf Link otwiera się w nowym oknie
Opis:: A cycle C is a vertex-dominating cycle if every vertex is adjacent to some vertex of C. Bondy and Fan [4] showed that if G is a 2-connected graph with δ(G) ≥ 1/3(|V(G)| - 4), then G has a vertex-dominating cycle. In this paper, we prove that if G is a 2-connected bipartite graph with partite sets V₁ and V₂ such that δ(G) ≥ 1/3(max{|V₁|,|V₂|} + 1), then G has a vertex-dominating cycle.
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: On arbitrarily vertex decomposable unicyclic graphs with dominating cycle
Autorzy:: Cichacz, Sylwia
Zioło, Irmina
Tematy:: arbitrarily vertex decomposable graph
dominating cycle; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743581.pdf Link otwiera się w nowym oknie
Opis:: A graph G of order n is called arbitrarily vertex decomposable if for each sequence (n₁,...,nₖ) of positive integers such that $∑^k_{i=1} n_i = n$, there exists a partition (V₁,...,Vₖ) of vertex set of G such that for every i ∈ {1,...,k} the set $V_i$ induces a connected subgraph of G on $n_i$ vertices. We consider arbitrarily vertex decomposable unicyclic graphs with dominating cycle. We also characterize all such graphs with at most four hanging vertices such that exactly two of them have a common neighbour.
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Research problems from the 18th Workshop '3in1' 2009
Autorzy:: Meszka, M. [ed.]
Tematy:: Hamilton-connected graph
hamiltonian graph
dominating cycle
bihomogeneously traceble graph; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/255619.pdf Link otwiera się w nowym oknie
Opis:: A collection of open problems that were posed at the 18th Workshop '3in1', held on November 26-28, 2009 in Krakow, Poland. The problems are presented by Zdenek Ryjacek in "Does the Thomassen's conjecture imply N=NP?" and "Dominating cycles and hamiltonian prisms", and by Carol T. Zamfirescu in "Two problems on bihomogeneously traceable digraphs".
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: Dominating sets and domination polynomials of certain graphs, II
Autorzy:: Alikhani, S.
Yee-hock, P.
Tematy:: domination polynomial
dominating set
cycle
theta graph; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/255942.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 5.

Tytuł:: 2-Connected Hamiltonian Claw-Free Graphs Involving Degree Sum of Adjacent Vertices
Autorzy:: Tian, Tao
Xiong, Liming
Tematy:: Hamiltonian cycle
degree sum
dominating closed trail
closure; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/32034090.pdf Link otwiera się w nowym oknie
Opis:: For a graph H, define $\overline{\sigma}_2(H)=min\{d(u)+d(v)|uv∈E(H)\}$. Let $H$ be a 2-connected claw-free simple graph of order $n$ with $\delta(H) ≥ 3$. In [J. Graph Theory 86 (2017) 193–212], Chen proved that if $\overline{\sigma}_2(H)≥\frac{n}{2}−1$ and $n$ is sufficiently large, then $H$ is Hamiltonian with two families of exceptions. In this paper, we refine the result. We focus on the condition $\overline{\sigma}_2(H)≥\frac{2n}{5}−1$, and characterize non-Hamiltonian 2-connected claw-free graphs $H$ of order $n$ sufficiently large with $\overline{\sigma}_2(H)≥\frac{2n}{5}−1$. As byproducts, we prove that there are exactly six graphs in the family of 2-edge-connected triangle-free graphs of order at most seven that have no spanning closed trail and give an improvement of a result of Veldman in [Discrete Math. 124 (1994) 229–239].
Dostawca treści:: Biblioteka Nauki

Artykuł

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