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Wyświetlanie 1-15 z 179
Tytuł:
On Independent [1, 2]-Sets in Trees
Autorzy:
Aleid, Sahar A.
Cáceres, José
Puertas, María Luz
Powiązania:
https://bibliotekanauki.pl/articles/31342284.pdf
Data publikacji:
2018-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination
independence
spanning trees
excellent trees
Opis:
An [1, k]-set S in a graph G is a dominating set such that every vertex not in S has at most k neighbors in it. If the additional requirement that the set must be independent is added, the existence of such sets is not guaranteed in every graph. In this paper we solve some problems previously posed by other authors about independent [1, 2]-sets. We provide a necessary condition for a graph to have an independent [1, 2]-set, in terms of spanning trees, and we prove that this condition is also sufficient for cactus graphs. We follow the concept of excellent tree and characterize the family of trees such that any vertex belongs to some independent [1, 2]-set. Finally, we describe a linear algorithm to decide whether a tree has an independent [1, 2]-set. This algorithm can be easily modified to obtain the cardinality of a smallest independent [1, 2]-set of a tree.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 3; 645-660
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Completely Independent Spanning Trees in (Partial) k-Trees
Autorzy:
Matsushita, Masayoshi
Otachi, Yota
Araki, Toru
Powiązania:
https://bibliotekanauki.pl/articles/31339419.pdf
Data publikacji:
2015-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
completely independent spanning trees
partial k-trees
Opis:
Two spanning trees T1 and T2 of a graph G are completely independent if, for any two vertices u and v, the paths from u to v in T1 and T2 are internally disjoint. For a graph G, we denote the maximum number of pairwise completely independent spanning trees by cist(G). In this paper, we consider cist(G) when G is a partial k-tree. First we show that ⌈k/2⌉ ≤ cist(G) ≤ k − 1 for any k-tree G. Then we show that for any p ∈ {⌈k/2⌉, . . ., k − 1}, there exist infinitely many k-trees G such that cist(G) = p. Finally we consider algorithmic aspects for computing cist(G). Using Courcelle’s theorem, we show that there is a linear-time algorithm that computes cist(G) for a partial k-tree, where k is a fixed constant.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 3; 427-437
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
European silver fir - an alternative for the dying Norway spruce in Bialowieza Forest?
Autorzy:
Marozau, Aleh
Mielcarek, Miłosz
Krok, Grzegorz
Paluch, Rafał
Chilinski, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/2041262.pdf
Data publikacji:
2021
Wydawca:
Instytut Badawczy Leśnictwa
Tematy:
artificial origin
old trees
adult generation
trees conditions
Opis:
The condition of Norway spruce (Picea abies (L.) Karst) in the Białowieża Forest is categorized as a crisis. It is believed that due to the cooling in the Holocene, the then-relict species of the forest, silver fir (Abies alba Mill.), disappeared from its ecosystems and then spruce appeared. Today’s climate change presents challenges to our civilization, including to forestry. However, there is no information at all about how this affected the silver fir in the Białowieża Forest. In the Polish part of the forest (subcompartment 498 Сi, Białowieża Forest District), for the first time a comprehensive study has been carried out on the condition of mature fir trees planted by man and on their progeny. The results indicate high forestry-taxation indicators of trees, resistance to the abiotic factor and competitiveness. Their constitution corresponds to local environmental conditions. However, the disproportionately small number of adult natural regeneration of old firs indicated some kind of malfunction in the mechanism of natural generational change.
Źródło:
Folia Forestalia Polonica. Series A . Forestry; 2021, 63, 2; 150-166
0071-6677
Pojawia się w:
Folia Forestalia Polonica. Series A . Forestry
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Arbitrarily vertex decomposable caterpillars with four or five leaves
Autorzy:
Cichacz, Sylwia
Görlich, Agnieszka
Marczyk, Antoni
Przybyło, Jakub
Woźniak, Mariusz
Powiązania:
https://bibliotekanauki.pl/articles/743967.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
arbitrarily vertex decomposable graphs
trees
caterpillars
star-like trees
Opis:
A graph G of order n is called arbitrarily vertex decomposable if for each sequence (a₁,...,aₖ) of positive integers such that a₁+...+aₖ = n there exists a partition (V₁,...,Vₖ) of the vertex set of G such that for each i ∈ {1,...,k}, $V_i$ induces a connected subgraph of G on $a_i$ vertices. D. Barth and H. Fournier showed that if a tree T is arbitrarily vertex decomposable, then T has maximum degree at most 4. In this paper we give a complete characterization of arbitrarily vertex decomposable caterpillars with four leaves. We also describe two families of arbitrarily vertex decomposable trees with maximum degree three or four.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 2; 291-305
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Smallest Harmonic Index of Trees with Given Maximum Degree
Autorzy:
Rasi, Reza
Sheikholeslami, Seyed Mahmoud
Powiązania:
https://bibliotekanauki.pl/articles/31342320.pdf
Data publikacji:
2018-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
harmonic index
trees
Opis:
The harmonic index of a graph G, denoted by H(G), is defined as the sum of weights 2/[d(u) + d(v)] over all edges uv of G, where d(u) denotes the degree of a vertex u. In this paper we establish a lower bound on the harmonic index of a tree T.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 2; 499-513
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Extensions of the minimum labelling spanning tree problem
Autorzy:
Cerulli, R.
Fink, A.
Gentili, M.
Voss, S.
Powiązania:
https://bibliotekanauki.pl/articles/308930.pdf
Data publikacji:
2006
Wydawca:
Instytut Łączności - Państwowy Instytut Badawczy
Tematy:
network design
metaheuristics
spanning trees
labelling trees
Steiner tree problem
Opis:
In this paper we propose some extensions of the minimum labelling spanning tree problem. The main focus is on the minimum labelling Steiner tree problem: given a graph G with a color (label) assigned to each edge, and a subset Q of the nodes of G (basic vertices), we look for a connected subgraph of G with the minimum number of different colors covering all the basic vertices. The problem has several applications in telecommunication networks, electric networks, multimodal transportation networks, among others, where one aims to ensure connectivity by means of homogeneous connections. Numerical results for several metaheuristics to solve the problem are presented.
Źródło:
Journal of Telecommunications and Information Technology; 2006, 4; 39-45
1509-4553
1899-8852
Pojawia się w:
Journal of Telecommunications and Information Technology
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Note: Sharp Upper and Lower Bounds on the Number of Spanning Trees in Cartesian Product of Graphs
Autorzy:
Azarija, Jernej
Powiązania:
https://bibliotekanauki.pl/articles/30098147.pdf
Data publikacji:
2013-09-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Cartesian product graphs
spanning trees
number of spanning trees
inequality
Opis:
Let $ G_1 $ and $ G_2 $ be simple graphs and let $ n_1 = |V (G_1)| $, $ m_1 = |E(G_1)| $ , $ n_2 = |V (G_2)|$ and $ m_2 = |E(G_2)|$. In this paper we derive sharp upper and lower bounds for the number of spanning trees $ \tau $ in the Cartesian product $ G_1 \square G_2 $ of $ G_1 $ and $ G_2 $. We show that: $$ \tau (G_1 \square G_2 ) \geq \frac{2(n_1-1)(n_2-1)}{n_1 n_2} (\tau (G_1) n_1 )^\frac{n_2+1}{2} (\tau(G_2)n_2)^\frac{n_1+1}{2} $$ and $$ \tau(G_1 \square G_2 ) \leq \tau (G_1) \tau (G_2) \left[ \frac{2m_1}{n_1-1} + \frac{2m_2}{n_2-1} \right]^{(n_1 - 1)(n_2 -1)} . $$ We also characterize the graphs for which equality holds. As a by-product we derive a formula for the number of spanning trees in $ K_{n_1} \square K_{n_2} $ which turns out to be $ n_1^{n_1-2} n_2^{n_2-2} (n_1 + n_2 )^{(n_1-1)(n_2-1)} $.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 4; 785-790
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monument trees in the Kampinos National Park (Central Poland): A review
Autorzy:
Szczepkowski, Andrzej
Tyburski, Łukasz
Sułkowska, Małgorzata
Powiązania:
https://bibliotekanauki.pl/articles/2041515.pdf
Data publikacji:
2020
Wydawca:
Instytut Badawczy Leśnictwa
Tematy:
Kampinos Forest
very large trees
venerable trees
natural monument
nature conservation
Opis:
The paper presents the history of the protection of trees with special values, the current state of monument trees and the preliminary description of trees meeting the minimal circumference criteria to be regarded as natural monuments in the Kampinos National Park (KNP). The study was conducted in the years 2017–2019. In the KNP, there are 69 living trees with a status of natural monuments. Most of them are oaks – 56 specimens, Scots pine – 6 specimens, small-leaved lime – 5 specimens and European hornbeam and European ash – 1 specimen each. Among all, 27 trees grow individually and the other 42 grow in 7 groups. About 200 trees were recognised as meeting the minimal circumference criteria to be regarded as natural monuments. The thickest size tree in the KNP is the black poplar with a circumference of 805 cm, growing in the enclave of Ruska Kępa, and the thickest monument tree in the KNP area is Dąb Kobędzy (Kobendza Oak) with a circumference of 582 cm. Almost a half of the living monument trees (34 specimens) are situated in Kampinos Forest District. In Kromnów, there are 20, and in Laski Forest District 15 specimens of monument trees are mapped. Living monument trees were found in 15 (out of 17) forest subdistricts. The highest number of monument trees was found in Rózin Forest Subdistrict (16) and in Wilków Forest Subdistrict (10). The lowest number – one specimen per forest subdistrict – was found in six forest subdistricts (Dąbrówka, Grabina, Janówek, Krzywa Góra, Rybitew and Zamczysko). In total, there are around 300 specimens of natural monuments and trees meeting the minimal circumference criteria to be regarded as natural monuments, which means that there is one tree of this category for each 125 ha surface of the KNP.
Źródło:
Folia Forestalia Polonica. Series A . Forestry; 2020, 62, 3; 210-219
0071-6677
Pojawia się w:
Folia Forestalia Polonica. Series A . Forestry
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on the p-domination number of trees
Autorzy:
Lu, Y.
Hou, X.
Xu, J.-M.
Powiązania:
https://bibliotekanauki.pl/articles/255183.pdf
Data publikacji:
2009
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
p-domination number
trees
Opis:
Let p be a positive integer and G = (V (G), E(G)) a graph. A p-dominating set of G is a subset S of V (G) such that every vertex not in S is dominated by at least p vertices in S. The p-domination number ϒp(G) is the minimum cardinality among the p-dominating sets of G. Let T be a tree with order n ≥ 2 and p ≥ 2 a positive integer. A vertex of V (T) is a p-leaf if it has degree at most p - 1, while a p-support vertex is a vertex of degree at least p adjacent to a p-leaf. In this note, we show that ϒp(T) ≥ (n + /Lp(T)/ - /Sp(T)/)/2, where Lp(T) and Sp(T) are the sets of p-leaves and p-support vertices of T, respectively. Moreover, we characterize all trees attaining this lower bound.
Źródło:
Opuscula Mathematica; 2009, 29, 2; 157-164
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the dominator colorings in trees
Autorzy:
Merouane, Houcine
Chellali, Mustapha
Powiązania:
https://bibliotekanauki.pl/articles/743280.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
dominator coloring
domination
trees
Opis:
In a graph G, a vertex is said to dominate itself and all its neighbors. A dominating set of a graph G is a subset of vertices that dominates every vertex of G. The domination number γ(G) is the minimum cardinality of a dominating set of G. A proper coloring of a graph G is a function from the set of vertices of the graph to a set of colors such that any two adjacent vertices have different colors. A dominator coloring of a graph G is a proper coloring such that every vertex of V dominates all vertices of at least one color class (possibly its own class). The dominator chromatic number $χ_d(G)$ is the minimum number of color classes in a dominator coloring of G. Gera showed that every nontrivial tree T satisfies $γ(T)+1 ≤ χ_d(T) ≤ γ(T)+2$. In this note we characterize nontrivial trees T attaining each bound.
Źródło:
Discussiones Mathematicae Graph Theory; 2012, 32, 4; 677-683
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Vertices Contained In All Or In No Minimum Semitotal Dominating Set Of A Tree
Autorzy:
Henning, Michael A.
Marcon, Alister J.
Powiązania:
https://bibliotekanauki.pl/articles/31341173.pdf
Data publikacji:
2016-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination
semitotal domination
trees
Opis:
Let G be a graph with no isolated vertex. In this paper, we study a parameter that is squeezed between arguably the two most important domination parameters; namely, the domination number, γ(G), and the total domination number, γt(G). A set S of vertices in a graph G is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number, γt2(G), is the minimum cardinality of a semitotal dominating set of G. We observe that γ(G) ≤ γt2(G) ≤ γt(G). We characterize the set of vertices that are contained in all, or in no minimum semitotal dominating set of a tree.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 1; 71-93
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Graphs with equal domination and 2-distance domination numbers
Autorzy:
Raczek, Joanna
Powiązania:
https://bibliotekanauki.pl/articles/743916.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination number
trees
unicyclic graphs
Opis:
Let G = (V,E) be a graph. The distance between two vertices u and v in a connected graph G is the length of the shortest (u-v) path in G. A set D ⊆ V(G) is a dominating set if every vertex of G is at distance at most 1 from an element of D. The domination number of G is the minimum cardinality of a dominating set of G. A set D ⊆ V(G) is a 2-distance dominating set if every vertex of G is at distance at most 2 from an element of D. The 2-distance domination number of G is the minimum cardinality of a 2-distance dominating set of G. We characterize all trees and all unicyclic graphs with equal domination and 2-distance domination numbers.
Źródło:
Discussiones Mathematicae Graph Theory; 2011, 31, 2; 375-385
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Unique Minimum Dominating Sets in Some Cartesian Product Graphs
Autorzy:
Hedetniemi, Jason T.
Powiązania:
https://bibliotekanauki.pl/articles/31339313.pdf
Data publikacji:
2015-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
vertex domination
graph products
trees
Opis:
Unique minimum vertex dominating sets in the Cartesian product of a graph with a complete graph are considered. We first give properties of such sets when they exist. We then show that when the first factor of the product is a tree, consideration of the tree alone is sufficient to determine if the product has a unique minimum dominating set.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 4; 615-628
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Graphs with Large Generalized (Edge-)Connectivity
Autorzy:
Li, Xueliang
Mao, Yaping
Powiązania:
https://bibliotekanauki.pl/articles/31340594.pdf
Data publikacji:
2016-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
(edge-)connectivity
Steiner tree
internally disjoint trees
edge-disjoint trees
packing
generalized (edge-)connectivity
Opis:
The generalized $k$-connectivity $ \kappa_k (G) $ of a graph $G$, introduced by Hager in 1985, is a nice generalization of the classical connectivity. Recently, as a natural counterpart, we proposed the concept of generalized $k$-edge-connectivity $ \lambda_k (G)$. In this paper, graphs of order $n$ such that $ \kappa_k (G) = n - k/2 - 1 $ and $ \lambda_k (G) = n - k/2 - 1 $ for even $k$ are characterized.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 4; 931-958
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On some families of arbitrarily vertex decomposable spiders
Autorzy:
Juszczyk, T.
Zioło, I. A.
Powiązania:
https://bibliotekanauki.pl/articles/254779.pdf
Data publikacji:
2010
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
arbitrarily vertex decomposable graph
trees
Opis:
A graph G of order n is called arbitrarily vertex decomposable if for each sequence (n1, . . . , nk) of positive integers such that [formula], there exists a partition (V1, . . . , Vk) of the vertex set of G such that for every i ∈ {1, . . . , k} the set Vi induces a connected subgraph of G on ni vertices. A spider is a tree with one vertex of degree at least 3. We characterize two families of arbitrarily vertex decomposable spiders which are homeomorphic to stars with at most four hanging edges.
Źródło:
Opuscula Mathematica; 2010, 30, 2; 147-154
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 179

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