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Search results for: CIRCULAR CHROMATIC NUMBER
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T-colorings, divisibility and circular chromatic number
PublicationLet T be a T-set, i.e., a finite set of nonnegative integers satisfying 0 ∈ T, and G be a graph. In the paper we study relations between the T-edge spans espT (G) and espd⊙T (G), where d is a positive integer and d ⊙ T = {0 ≤ t ≤ d (max T + 1): d |t ⇒ t/d ∈ T} . We show that espd⊙T (G) = d espT (G) − r, where r, 0 ≤ r ≤ d − 1, is an integer that depends on T and G. Next we focus on the case T = {0} and show that espd⊙{0} (G) =...
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The circular chromatic index of some class 2 graphs
PublicationW artykule został wyznaczony cyrkularny indeks chromatyczny dla dwóch rodzin grafów klasy 2. Co więcej, podano nie trywialne oszacowania tego parametru dla snarków Isaacsa i Goldberga. Na koniec artykułu rozważana jest złożoność obliczeniowa problemów związanych z cyrkularnym kolorowaniem krawędzi.
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Total chromatic sum for trees
PublicationThe total chromatic sum of a graph is the minimum sum of colors (natural numbers) taken over all proper colorings of vertices and edges of a graph. We provide infinite families of trees for which the minimum number of colors to achieve the total chromatic sum is equal to the total chromatic number. We construct infinite families of trees for which these numbers are not equal, disproving the conjecture from 2012.
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Infinite chromatic games
PublicationIn the paper we introduce a new variant of the graph coloring game and a new graph parameter being the result of the new game. We study their properties and get some lower and upper bounds, exact values for complete multipartite graphs and optimal, often polynomial-time strategies for both players provided that the game is played on a graph with an odd number of vertices. At the end we show that both games, the new and the classic...
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A 27/26-approximation algorithm for the chromatic sum coloring of bipartitegraphs
PublicationWe consider the CHROMATIC SUM PROBLEM on bipartite graphs which appears to be much harder than the classical CHROMATIC NUMBER PROBLEM. We prove that the CHROMATIC SUM PROBLEM is NP-complete on planar bipartite graphs with Delta less than or equal to 5, but polynomial on bipartite graphs with Delta less than or equal to 3, for which we construct an O(n(2))-time algorithm. Hence, we tighten the borderline of intractability for this...
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2-Coloring number revisited
Publication2-Coloring number is a parameter, which is often used in the literature to bound the game chromatic number and other related parameters. However, this parameter has not been precisely studied before. In this paper we aim to fill this gap. In particular we show that the approximation of the game chromatic number by the 2-coloring number can be very poor for many graphs. Additionally we prove that the 2-coloring number may grow...
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Relations between the domination parameters and the chromatic index of a graph
PublicationIn this paper we show bounds for the sum and the product of the domination parameters and the chromatic index of a graph. We alsopresent some families of graphs for which these bounds are achieved.
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Process Engineering in Circular Economy
e-Learning CoursesKurs jest przeznaczony dla doktorantów szkoły doktorskiej w dyscyplnach: inżynieria lądowa i transport (SzD), III stopnia, stacjonarne inżynieria środowiska, górnictwo i energetyka (SzD), III stopnia, stacjonarne The course is addressed to PhD students of the doctoral school in disciplines: civil engineering and transport environmental engineering, mining and power engineering Course type: lecture Total hours of...
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Process engineering in circular economy
e-Learning CoursesDefinition and principles of the circular economy (CE). The transition from a linear model to a circular model. Business models for the CE. Circular design and innovation. CE assessment carbon footprint, life cycle assessment. Case studies of the cities implementing the CE concept. CE policy and legislation (EU and Poland). Wastewater treatment plants as an element of the CE. Energy and nutrient recovery technologies in wastewater...
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Process engineering in circular economy 22/23
e-Learning CoursesBackground of the circular economy What is the circular economy? (Definition) How is the circular economy different from a linear economy? How do materials circulate in the circular economy? The circular economy and sustainable development How to measure circularity? Link between the circular economy and life cycle assessment (LCA) What are the benefits of the circular economy? The circular economy policies and governance Wastewater...
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Circular Farmaceutica
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Isolation Number versus Domination Number of Trees
PublicationIf G=(VG,EG) is a graph of order n, we call S⊆VG an isolating set if the graph induced by VG−NG[S] contains no edges. The minimum cardinality of an isolating set of G is called the isolation number of G, and it is denoted by ι(G). It is known that ι(G)≤n3 and the bound is sharp. A subset S⊆VG is called dominating in G if NG[S]=VG. The minimum cardinality of a dominating set of G is the domination number, and it is denoted by γ(G)....
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Circular saw vibrations or dynamics of the spindle
PublicationSawing of wood with circular saws is a typical example of cutting with multi-blade tools. In that kind of cutting, theposition accuracy of following tool blades is a crucial factor which affects the cutting process and machining final effects.Position tooth errors may cause deterioration in cutting conditions, changes in loads of individual teeth and the tool as a whole,and also a decrease in accuracy and surface quality after...
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[ILiT, IŚGiE] Process engineering in circular economy - Nowy
e-Learning CoursesKurs jest przeznaczony dla doktorantów szkoły doktorskiej w dyscyplnach: inżynieria lądowa i transport (SzD), III stopnia, stacjonarne inżynieria środowiska, górnictwo i energetyka (SzD), III stopnia, stacjonarne The course is addressed to PhD students of the doctoral school in disciplines: civil engineering and transport environmental engineering, mining and power engineering Course type: lecture Total hours of...
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Chromatic scheduling in a cyclic open shop
PublicationPraca jest poświęcona złożoności obliczeniowej problemu cyklicznego szeregowania w systemie otwartym. Autorzy analizując wykazują, że problem jest NP-trudny dla 3 procesorów i konstruują algorytm dokładny dla przypadku dwóch procesorów.Ponadto analizowany jest zwarty wariant cyklicznego systemu otwartego. W tym przypadku autorzy pokazują, że już szeregowanie na dwóch procesorach prowadzi do problemu NP-trudnego.
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MACHINE VISION DETECTION OF THE CIRCULAR SAW VIBRATIONS
PublicationDynamical properties of rotating circular saw blades are crucial for both production quality and personnel safety. This paper presents a novel method for monitoring circular saw vibrations and deviations. A machine vision system uses a camera and a laser line projected on the saw’s surface to estimate vibration range. Changes of the dynamic behaviour of the saw were measured as a function of the rotational speed. The critical rotational...
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ICT-enabled circular economy: conceptualising the links
PublicationThis chapter sets conceptual backgrounds regarding the potentially emerging causal links between digital technologies and circular economy ideas implementation. We argue that digital technologies may constitute an effective element enabling the transformation from linear to circular and environmentally friendly economic activities. This work draws the general picture at the macro and micro level. The macro perspective shows how...
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Chromatic cost coloring of weighted bipartite graphs
PublicationGiven a graph G and a sequence of color costs C, the Cost Coloring optimization problem consists in finding a coloring of G with the smallest total cost with respect to C. We present an analysis of this problem with respect to weighted bipartite graphs. We specify for which finite sequences of color costs the problem is NP-hard and we present an exact polynomial algorithm for the other finite sequences. These results are then extended...
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On trees with double domination number equal to 2-domination number plus one
PublicationA vertex of a graph is said to dominate itself and all of its neighbors. A subset D subseteq V(G) is a 2-dominating set of G if every vertex of V(G)D is dominated by at least two vertices of D, while it is a double dominating set of G if every vertex of G is dominated by at least two vertices of D. The 2-domination (double domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (double dominating,...
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On trees with double domination number equal to total domination number plus one
PublicationA total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The total (double, respectively) domination number of a graph G is the minimum cardinality of a total (double,...
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Bondage number of grid graphs
PublicationThe bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than the domination number of G. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some strong product and direct product of two paths.
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[ILiT, IŚGiE] Process engineering in circular economy 20/21 Summer
e-Learning CoursesKurs jest przeznaczony dla doktorantów szkoły doktorskiej w dyscyplnach: inżynieria lądowa i transport (SzD), III stopnia, stacjonarne inżynieria środowiska, górnictwo i energetyka (SzD), III stopnia, stacjonarne The course is addressed to PhD students of the doctoral school in disciplines: civil engineering and transport environmental engineering, mining and power engineering Course type: lecture Total hours of...
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Economical wood sawing with circular saw blades
PublicationMaterial- and energy-saving belong to the basic requirements which are imposed on the contemporary manufacturing processes. Since realization of those processes gives measurable profits not only economical but also ecological. In case of wood sawing with circular saw blades material- and energy-savings are dependent on total overall set of teeth (theoretical kerf) and teeth position accuracy in relation to the workpiece. Hence,...
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Bounds on isolated scattering number
PublicationThe isolated scattering number is a parameter that measures the vulnerability of networks. This measure is bounded by formulas de- pending on the independence number. We present new bounds on the isolated scattering number that can be calculated in polynomial time.
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Bounds on isolated scattering number
PublicationThe isolated scattering number is a parameter that measures the vulnerability of networks. This measure is bounded by formulas de- pending on the independence number. We present new bounds on the isolated scattering number that can be calculated in polynomial time.
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Navier number and transition to turbulence
PublicationThe motivation behind this article is to explain a role of the Navier number (Na -dimensionless slip-length) in prediction of closures for laminar to turbulent transition undergoing via eddies detachment from the slip layer in nano-cannals. Additionally the role of the Navier number Na in universal modeling of phenomenon of enhanced mass flow rate reported in micro- and nano-channels has been explained. The Na number should be...
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On trees with double domination number equal to 2-outer-independent domination number plus one
PublicationA vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. For a graph G=(V,E), a subset D subseteq V(G) is a 2-dominating set if every vertex of V(G)D has at least two neighbors...
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Edge-chromatic sum of trees and bounded cyclicity graphs
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On domination multisubdivision number of unicyclic graphs
PublicationThe paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009), 622–628], we constructively characterize all connected unicyclic graphs with...
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TOTAL DOMINATION MULTISUBDIVISION NUMBER OF A GRAPH
PublicationThe domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. Similarly we define the total domination multisubdivision number msd_t (G) of a graph G and we show that for any connected graph G of order at least two, msd_t (G) ≤ 3. We show that for trees the total domination...
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A design framework for rigorous constrained EM-driven optimization of miniaturized antennas with circular polarization
PublicationCompact radiators with circular polarization are important components of modern mobile communication systems. Their design is a challenging process which requires maintaining simultaneous control over several performance figures but also the structure size. In this work, a novel design framework for multi-stage constrained miniaturization of antennas with circular polarization is presented. The method involves sequential optimization...
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Some variants of perfect graphs related to the matching number, the vertex cover and the weakly connected domination number
PublicationGiven two types of graph theoretical parameters ρ and σ, we say that a graph G is (σ, ρ)- perfect if σ(H) = ρ(H) for every non-trivial connected induced subgraph H of G. In this work we characterize (γw, τ )-perfect graphs, (γw, α′)-perfect graphs, and (α′, τ )-perfect graphs, where γw(G), τ (G) and α′(G) denote the weakly connected domination number, the vertex cover number and the matching number of G, respectively. Moreover,...
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The convex domination subdivision number of a graph
PublicationLet G = (V;E) be a simple graph. A set D\subset V is a dominating set of G if every vertex in V - D has at least one neighbor in D. The distance d_G(u, v) between two vertices u and v is the length of a shortest (u, v)-path in G. An (u, v)-path of length d_G(u; v) is called an (u, v)-geodesic. A set X\subset V is convex in G if vertices from all (a, b)-geodesics belong to X for any two vertices a, b \in X. A set X is a convex dominating...
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The reduction of vibrations in circular sawing machines
PublicationThe presented in this paper the main objectives of the research were to explore vibrations signals of the main spindle system, the machine tool body and a circular saw to extract informative features for assessment of the designs of the panel saw Fx3 and its follower Fx550.Even though the main spindle of the new table sliding saw Fx550 has its rotational speeds larger about 20% in comparison to the Fx3, peak values of the vibrational...
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Comparison of natural frequencies of a circular saw blade obtained empirically and with FEM
PublicationThe knowledge of the natural frequencies’ values of circular saw blades is necessary to determine the minimal critical rotational speed in which they can work with required stability. Moreover, testing the circular saw blades with more complicated shapes, e.g. which have additional holes inside blades for cleaning knifes or additional indirect teeth in gullets, reveals some kind of problematic properties of these saw blades. The...
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Similarities and Differences Between the Vertex Cover Number and the Weakly Connected Domination Number of a Graph
PublicationA vertex cover of a graph G = (V, E) is a set X ⊂ V such that each edge of G is incident to at least one vertex of X. The ve cardinality of a vertex cover of G. A dominating set D ⊆ V is a weakly connected dominating set of G if the subgraph G[D]w = (N[D], Ew) weakly induced by D, is connected, where Ew is the set of all edges having at least one vertex in D. The weakly connected domination number γw(G) of G is the minimum cardinality...
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Weakly convex domination subdivision number of a graph
PublicationA set X is weakly convex in G if for any two vertices a; b \in X there exists an ab–geodesic such that all of its vertices belong to X. A set X \subset V is a weakly convex dominating set if X is weakly convex and dominating. The weakly convex domination number \gamma_wcon(G) of a graph G equals the minimum cardinality of a weakly convex dominating set in G. The weakly convex domination subdivision number sd_wcon (G) is the minimum...
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Influence of edge subdivision on the convex domination number
PublicationWe study the influence of edge subdivision on the convex domination number. We show that in general an edge subdivision can arbitrarily increase and arbitrarily decrease the convex domination number. We also find some bounds for unicyclic graphs and we investigate graphs G for which the convex domination number changes after subdivision of any edge in G.
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Influence of electrode geometric arrangement on the operation of narrow circular electrostatic precipitator
PublicationIn this work the influence of electrode geometric arrangement on the operation of a circular electrostatic precipitator (ESP) was investigated using Particle Image Velocimetry (PIV) method. The ESP was a glass circular cylinder (29 mm in diameter, 300 mm long) equipped with a wire discharge electrode and circular-cylinder collecting electrode. The stainless-steel discharge wire electrode (0.23 mm in diameter, 100 mm long) was mounted...
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Research in Number Theory
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Algebra & Number Theory
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JOURNAL OF NUMBER THEORY
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On the super domination number of lexicographic product graphs
PublicationThe neighbourhood of a vertexvof a graphGis the setN(v) of all verticesadjacent tovinG. ForD⊆V(G) we defineD=V(G)\D. A setD⊆V(G) is called a super dominating set if for every vertexu∈D, there existsv∈Dsuch thatN(v)∩D={u}. The super domination number ofGis theminimum cardinality among all super dominating sets inG. In this article weobtain closed formulas and tight bounds for the super dominating number oflexicographic product...
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Coronas and Domination Subdivision Number of a Graph
PublicationIn this paper, for a graph G and a family of partitions P of vertex neighborhoods of G, we define the general corona G ◦P of G. Among several properties of this new operation, we focus on application general coronas to a new kind of characterization of trees with the domination subdivision number equal to 3.
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Novel strategies to enhance hydrodynamic cavitation in a circular venturi using RANS numerical simulations
PublicationHydrodynamic cavitation is a popular advanced oxidation technique and it has received wide range of applications from waste water treatment to the nanoparticles synthesis in recent years. The enhancement of the intensity of the hydrodynamic cavitation is always been an emerging field of research. Within this framework, we have proposed and investigated three distinct strategies to enhance the intensity of cavitation in a circular...
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THE USE OF FEM FOR DETERMINATION OF RESONANT FREQUENCIES OF CIRCULAR SAW BLADES WITH INDIRECT TEETH IN GULLETS
PublicationUnderstanding the dynamical properties of the circular saw blade is necessary, since, there is a really need for a stable work at working rotational speeds, which are determined by frequencies at which the circular saw blade tends to vibrate. It was observed that the resonant frequency depend on the circular saw blade shape, a collar diameter and on saw’s teeth shape. In the presented work an attention was paid to the effect of...
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U.S. Geological Survey Circular
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Introduction to smart solutions for wastewater: Road-mapping the transition to circular economy
PublicationToday there is an urgent need to move from a linear to a circular economy approach with special focus to water and environment. Despite the paramount importance, this transition is hampered by barriers which concern not only technological but embrace also organizational, regulatory, social, and economic aspects. In order to overcome such barriers, innovative water-smart solutions are needed and a robust roadmap for the transition...
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Sustainable Waste Management for Implementation of a Circular Economy Model in a Port
PublicationThe manuscript presents the management of waste from marine vessels and cargo handling companies in a selected European Union port. The main objective of the paper is to analyse and evaluate the existing waste management model in the port of Szczecin in the context of circular economy. The expert research carried out is aimed, inter alia, at identifying which of the solutions currently in use need to be improved from an environmental...
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Process engineering in circular economy
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