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Tytuł:
Graphs that are Critical for the Packing Chromatic Number
Autorzy:
Brešar, Boštjan
Ferme, Jasmina
Powiązania:
https://bibliotekanauki.pl/articles/32318620.pdf
Data publikacji:
2022-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
packing coloring
critical graph
diameter
block graph
tree
Opis:
Given a graph G, a coloring c : V (G) → {1, …, k} such that c(u) = c(v) = i implies that vertices u and v are at distance greater than i, is called a packing coloring of G. The minimum number of colors in a packing coloring of G is called the packing chromatic number of G, and is denoted by χρ(G). In this paper, we propose the study of χρ-critical graphs, which are the graphs G such that for any proper subgraph H of G, χρ(H) < χρ(G). We characterize χρ-critical graphs with diameter 2, and χρ-critical block graphs with diameter 3. Furthermore, we characterize χρ-critical graphs with small packing chromatic number, and we also consider χρ-critical trees. In addition, we prove that for any graph G and every edge e ∈ E(G), we have (χρ(G)+1)/2 ≤ χρ(G−e) ≤ χρ(G), and provide a corresponding realization result, which shows that χρ(G − e) can achieve any of the integers between these bounds.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 2; 569-589
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nowhere-Zero Unoriented 6-Flows on Certain Triangular Graphs
Autorzy:
Yang, Fan
Li, Liangchen
Zhou, Sizhong
Powiązania:
https://bibliotekanauki.pl/articles/32309450.pdf
Data publikacji:
2022-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
nowhere-zero k -flow
triangle-tree
triangle-star
bidirected graph
Opis:
A nowhere-zero unoriented flow of graph G is an assignment of non-zero real numbers to the edges of G such that the sum of the values of all edges incident with each vertex is zero. Let k be a natural number. A nowhere-zero unoriented k-flow is a flow with values from the set {±1, . . ., ±(k − 1)}, for short we call it NZ-unoriented k-flow. Let H1 and H2 be two graphs, H1⊕H2 denote the 2-sum of H1 and H2, if E(H1⊕H2) = E(H1) ∪ E(H2), |V(H1)∩V(H2)|=2, and |E(H1)∩E(H2)| = 1. A triangle-path in a graph G is a sequence of distinct triangles T1, T2, . . ., Tm in G such that for 1 ≤ i ≤ m, |E(Ti)∩E(Ti+1)| = 1 and E(Ti)∩E(Tj)=∅ if j>i+1. A triangle-star is a graph with triangles such that each triangle having one common edges with other triangles. Let G be a graph which can be partitioned into some triangle-paths or wheels H1, H2, . . ., Ht such that G = H1⊕H2⊕...⊕Ht. In this paper, we prove that G except a triangle-star admits an NZ-unoriented 6-flow. Moreover, if each Hi is a triangle-path, then G except a triangle-star admits an NZ-unoriented 5-flow.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 3; 727-746
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Ambarzumian type theorems for tree domains
Autorzy:
Pivovarchik, Vyacheslav
Powiązania:
https://bibliotekanauki.pl/articles/2216192.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Sturm-Liouville equation
eigenvalue
equilateral tree
star graph
Dirichlet boundary condition
Neumann boundary condition
Opis:
It is known that the spectrum of the spectral Sturm–Liouville problem on an equilateral tree with (generalized) Neumann’s conditions at all vertices uniquely determines the potentials on the edges in the unperturbed case, i.e. case of the zero potentials on the edges (Ambarzumian’s theorem). This case is exceptional, and in general case (when the Dirichlet conditions are imposed at some of the pendant vertices) even two spectra of spectral problems do not determine uniquely the potentials on the edges. We consider the spectral Sturm–Liouville problem on an equilateral tree rooted at its pendant vertex with (generalized) Neumann conditions at all vertices except of the root and the Dirichlet condition at the root. In this case Ambarzumian’s theorem can’t be applied. We show that if the spectrum of this problem is unperturbed, the spectrum of the Neumann-Dirichlet problem on the root edge is also unperturbed and the spectra of the problems on the complimentary subtrees with (generalized) Neumann conditions at all vertices except the subtrees’ roots and the Dirichlet condition at the subtrees’ roots are unperturbed then the potential on each edge of the tree is 0 almost everywhere.
Źródło:
Opuscula Mathematica; 2022, 42, 3; 427-437
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Packing Trees in Complete Bipartite Graphs
Autorzy:
Wang, Jieyan
Powiązania:
https://bibliotekanauki.pl/articles/32361740.pdf
Data publikacji:
2022-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
packing
placement
edge-disjoint tree
bipartite graph
Opis:
An embedding of a graph H in a graph G is an injection (i.e., a one-to-one function) σ from the vertices of H to the vertices of G such that σ(x)σ(y) is an edge of G for all edges xy of H. The image of H in G under σ is denoted by σ(H). A k-packing of a graph H in a graph G is a sequence (σ1, σ2,…, σk) of embeddings of H in G such that σ1(H), σ2(H),…, σk(H) are edge disjoint. We prove that for any tree T of order n, there is a 4-packing of T in a complete bipartite graph of order at most n+12.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 1; 263-275
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Upper bounds on distance vertex irregularity strength of some families of graphs
Autorzy:
Cichacz, Sylwia
Görlich, Agnieszka
Semaničová-Feňovčíková, Andrea
Powiązania:
https://bibliotekanauki.pl/articles/2216229.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
distance vertex irregularity strength of a graph
hypercube
tree
graph
Opis:
For a graph G its distance vertex irregularity strength is the smallest integer k for which one can find a labeling f : V (G) → {1, 2, . . . , k} such that $ \sum_{x \in N(v)} f(x) \neq \sum_{x \in N(u)} f(x) $ for all vertices u, v of G, where N(v) is the open neighborhood of v. In this paper we present some upper bounds on distance vertex irregularity strength of general graphs. Moreover, we give upper bounds on distance vertex irregularity strength of hypercubes and trees.
Źródło:
Opuscula Mathematica; 2022, 42, 4; 561--571
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
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:
ℤ2 × ℤ2 -Cordial Cycle-Free Hypergraphs
Autorzy:
Cichacz, Sylwia
Görlich, Agnieszka
Tuza, Zsolt
Powiązania:
https://bibliotekanauki.pl/articles/32361757.pdf
Data publikacji:
2021-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
V 4 -cordial graph
hypergraph
labeling of hypergraph
hyper-tree
Opis:
Hovey introduced A-cordial labelings as a generalization of cordial and harmonious labelings [7]. If A is an Abelian group, then a labeling f : V (G) → A of the vertices of some graph G induces an edge labeling on G; the edge uv receives the label f(u) + f(v). A graph G is A-cordial if there is a vertex-labeling such that (1) the vertex label classes differ in size by at most one and (2) the induced edge label classes differ in size by at most one. The problem of A-cordial labelings of graphs can be naturally extended for hypergraphs. It was shown that not every 2-uniform hypertree (i.e., tree) admits a ℤ2 × ℤ2-cordial labeling [8]. The situation changes if we consider p-uniform hypertrees for a bigger p. We prove that a p-uniform hypertree is ℤ2 × ℤ2-cordial for any p > 2, and so is every path hypergraph in which all edges have size at least 3. The property is not valid universally in the class of hypergraphs of maximum degree 1, for which we provide a necessary and sufficient condition.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 4; 1021-1040
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of game tree structures in the process of obtaining knowledge
Autorzy:
Deptuła, Adam
Powiązania:
https://bibliotekanauki.pl/articles/1878717.pdf
Data publikacji:
2020
Wydawca:
Politechnika Śląska. Wydawnictwo Politechniki Śląskiej
Tematy:
dependence graph
tree structure
artificial intelligence
optimization
wykres zależności
struktura drzewiasta
sztuczna inteligencja
optymalizacja
Opis:
Purpose: The purpose of the article is to present dependency graphs and parametric game tree structures as tools in generating and acquiring knowledge. Design/methodology/approach: The thematic scope of work concerns the author's method of generating graphs and decision trees. The scope of work includes the analysis of computational assumptions of guidelines supporting knowledge generation and decision making. Findings: The paper presents a method of generating game tree structures that allow to change the values of decision parameters in the issues of decision making and knowledge generation. Research limitations/implications: Further development directions of the presented issues should be conducted in the field of computer implementation of the developed algorithms. Practical implications: The most important in this regard will be the selection of the optimal programming environment with the possibility of installing the program in laboratory room systems for decision support and knowledge management for students. At a later stage, the use of tools in various problems in companies with a managerial and technical profile. Social implications: The application of method can improve the quality of decision alignment and give access to problem solving of various technical problems. Originality/value: A novelty is the use of parametric game tree structures as an alternative method to induction trees and multi-valued logical trees. Because game structures, unlike other methods, are built directly from the graph.
Źródło:
Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska; 2020, 144; 43-57
1641-3466
Pojawia się w:
Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Conflict-Free Vertex-Connections of Graphs
Autorzy:
Li, Xueliang
Zhang, Yingying
Zhu, Xiaoyu
Mao, Yaping
Zhao, Haixing
Jendrol’, Stanislav
Powiązania:
https://bibliotekanauki.pl/articles/31868621.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
vertex-coloring
conflict-free vertex-connection
2-connected graph
tree
Opis:
A path in a vertex-colored graph is called conflict-free if there is a color used on exactly one of its vertices. A vertex-colored graph is said to be conflict-free vertex-connected if any two vertices of the graph are connected by a conflict-free path. This paper investigates the question: for a connected graph G, what is the smallest number of colors needed in a vertex-coloring of G in order to make G conflict-free vertex-connected. As a result, we get that the answer is easy for 2-connected graphs, and very difficult for connected graphs with more cut-vertices, including trees.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 51-65
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Decompositions of Cubic Traceable Graphs
Autorzy:
Liu, Wenzhong
Li, Panpan
Powiązania:
https://bibliotekanauki.pl/articles/31867897.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
decomposition
cubic traceable graph
spanning tree
matching
2-regular graph
Opis:
A traceable graph is a graph with a Hamilton path. The 3-Decomposition Conjecture states that every connected cubic graph can be decomposed into a spanning tree, a 2-regular graph and a matching. We prove the conjecture for cubic traceable graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 35-49
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Logical classification trees in recognition problems
Logiczne drzewa klasyfikacji w zadaniach rozpoznawania
Autorzy:
Povhan, Igor
Powiązania:
https://bibliotekanauki.pl/articles/408473.pdf
Data publikacji:
2020
Wydawca:
Politechnika Lubelska. Wydawnictwo Politechniki Lubelskiej
Tematy:
pattern recognition problem
logical tree
graph-scheme model
recognition system
zadanie rozpoznawania obrazów
drzewo logiczne
schemat modeli rozpoznawania
system rozpoznawania
Opis:
The paper is dedicated to algorithms for constructing a logical tree of classification. Nowadays, there exist many algorithms for constructing logical classification trees. However, all of them, as a rule, are reduced to the construction of a single classification tree based on the data of a fixed training sample. There are very few algorithms for constructing recognition trees that are designed for large data sets. It is obvious that such sets have objective factors associated with the peculiarities of the generation of such complex structures, methods of working with them and storage. In this paper, we focus on the description of the algorithm for constructing classification trees for a large training set and show the way to the possibility of a uniform description of a fixed class of recognition trees. A simple, effective, economical method of constructing a logical classification tree of the training sample allows you to provide the necessary speed, the level of complexity of the recognition scheme, which guarantees a simple and complete recognition of discrete objects.
Artykuł poświęcono algorytmom konstruowania logicznych drzew klasyfikacji. Większość tych algorytmów z reguły sprowadzają się do zbudowania jednego drzewa klasyfikacyjnego na podstawie stałej próby uczącej. Należy zauważyć, że niewiele algorytmów budowania drzew klasyfikacyjnych dla prób treningowych o dużej objętości. Oczywiste jest, że mają one obiektywne czynniki związane ze specyfi ką generowania takich struktur, metodami pracy z nimi i ich przechowywania. W niniejszym artykule autorzy skupiają się na opisie algorytmu konstruowania drzew klasyfikacyjnych dla dużego zbioru uczącego i wskazują możliwość jednolitego opisu stałej klasy drzew rozpoznawczych. Prosta, skuteczna i ekonomiczna metoda budowy logicznego drzewa klasyfikacyjnego dla danej próby uczącej pozwala na zapewnienie niezbędnej szybkości i stopnia złożoności schematu rozpoznawania, co gwarantuje proste i kompletne rozpoznawanie obiektów dyskretnych.
Źródło:
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska; 2020, 10, 2; 12-15
2083-0157
2391-6761
Pojawia się w:
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Minimum Number of Spanning Trees in Cubic Multigraphs
Autorzy:
Bogdanowicz, Zbigniew R.
Powiązania:
https://bibliotekanauki.pl/articles/32083837.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cubic multigraph
spanning tree
regular graph
enumeration
Opis:
Let G2n, H2n be two non-isomorphic connected cubic multigraphs of order 2n with parallel edges permitted but without loops. Let t(G2n), t (H2n) denote the number of spanning trees in G2n, H2n, respectively. We prove that for n ≥ 3 there is the unique G2n such that t(G2n) < t(H2n) for any H2n. Furthermore, we prove that such a graph has t(G2n) = 522n−3 spanning trees. Based on our results we give a conjecture for the unique r-regular connected graph H2n of order 2n and odd degree r that minimizes the number of spanning trees.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 149-159
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Trees as Star Complements in Regular Graphs
Autorzy:
Rowlinson, Peter
Powiązania:
https://bibliotekanauki.pl/articles/31562766.pdf
Data publikacji:
2020-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
eigenvalue
regular graph
star complement
tree
Opis:
Let G be a connected r-regular graph (r > 3) of order n with a tree of order t as a star complement for an eigenvalue µ ∉ {−1, 0}. It is shown that n ≤ 1/2 (r + 1)t − 2. Equality holds when G is the complement of the Clebsch graph (with µ = 1, r = 5, t = 6, n = 16).
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 2; 621-636
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Trees with Distinguishing Index Equal Distinguishing Number Plus One
Autorzy:
Alikhani, Saeid
Klavžar, Sandi
Lehner, Florian
Soltani, Samaneh
Powiązania:
https://bibliotekanauki.pl/articles/31804165.pdf
Data publikacji:
2020-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
automorphism group
distinguishing index
distinguishing number
tree
unicyclic graph
Opis:
The distinguishing number (index) D(G) (D′ (G)) of a graph G is the least integer d such that G has an vertex (edge) labeling with d labels that is preserved only by the trivial automorphism. It is known that for every graph G we have D′ (G) ≤ D(G) + 1. In this note we characterize finite trees for which this inequality is sharp. We also show that if G is a connected unicyclic graph, then D′ (G) = D(G).
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 3; 875-884
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of complex game-tree structures for the Hsu graph in the analysis of automatic transmission gearboxes
Autorzy:
Deptula, A.
Partyka, M. A.
Powiązania:
https://bibliotekanauki.pl/articles/99927.pdf
Data publikacji:
2018
Wydawca:
Wrocławska Rada Federacji Stowarzyszeń Naukowo-Technicznych
Tematy:
automatic transmissions gearboxes
Hsu graph
optimization
game-tree structures
computer analysis
Opis:
In the article was discussed the possibility of structures and information systems complex game trees for the analysis of automatic gearboxes. The purpose of modelling an automatic gearbox with graphs can be versatile, namely: determining the transmission ratio of individual gears, analysing the speed and acceleration of individual rotating elements. In a further step, logic tree-decision methods can be used to analyse functional schemes of selected transmission gears. Instead, for graphs that are models of transmission, parametrically acting tree structures can be used. This allows for the generalization and extension of the algorithmic approach, furthermore in the future it will allow further analyses and syntheses, such as checking the isomorphism of the proposed solutions, determining the validity of construction and / or operating parameters of the analysed gears. The game tree structure describes a space of possible solutions in order to find optimum objective functions. There is the connection with other graphical structures which can be graphs in another sense, or even decision trees with node and/or branch coding.
Źródło:
Journal of Machine Engineering; 2018, 18, 4; 96-113
1895-7595
2391-8071
Pojawia się w:
Journal of Machine Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 46

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