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Total Domination Versus Domination in Cubic Graphs
PublikacjaA dominating set in a graph G is a set S of vertices of G such that every vertex not in S has a neighbor in S. Further, if every vertex of G has a neighbor in S, then S is a total dominating set of G. The domination number,γ(G), and total domination number, γ_t(G), are the minimum cardinalities of a dominating set and total dominating set, respectively, in G. The upper domination number, \Gamma(G), and the upper total domination...
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Non-isolating bondage in graphs
PublikacjaA dominating set of a graph $G = (V,E)$ is a set $D$ of vertices of $G$ such that every vertex of $V(G) \setminus D$ has a neighbor in $D$. The domination number of a graph $G$, denoted by $\gamma(G)$, is the minimum cardinality of a dominating set of $G$. The non-isolating bondage number of $G$, denoted by $b'(G)$, is the minimum cardinality among all sets of edges $E' \subseteq E$ such that $\delta(G-E') \ge 1$ and $\gamma(G-E')...
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Reconfiguring Minimum Dominating Sets in Trees
PublikacjaWe provide tight bounds on the diameter of γ-graphs, which are reconfiguration graphs of the minimum dominating sets of a graph G. In particular, we prove that for any tree T of order n ≥ 3, the diameter of its γ-graph is at most n/2 in the single vertex replacement adjacency model, whereas in the slide adjacency model, it is at most 2(n − 1)/3. Our proof is constructive, leading to a simple linear-time algorithm for determining...
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Parity vertex colouring of graphs
PublikacjaA parity path in a vertex colouring of a graph is a path along which each colour is used an even number of times. Let Xp(G) be the least number of colours in a proper vertex colouring of G having no parity path. It is proved that for any graph G we have the following tight bounds X(G) <= Xp(G) <=|V(G)|− a(G)+1, where X(G) and a(G) are the chromatic number and the independence number of G, respectively. The bounds are improved for...
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An Efficient Noisy Binary Search in Graphs via Median Approximation
PublikacjaConsider a generalization of the classical binary search problem in linearly sorted data to the graph-theoretic setting. The goal is to design an adaptive query algorithm, called a strategy, that identifies an initially unknown target vertex in a graph by asking queries. Each query is conducted as follows: the strategy selects a vertex q and receives a reply v: if q is the target, then =, and if q is not the target, then v is a...
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Comparison of noise reduction methods in radiometric correlation measurements of two-phase liquid-gas flows
PublikacjaTwo-phase liquid-gas flows occur frequently in the mining, energy, chemical, and petrochemical industries. One of non-contact methods used to analyse these flows is the gamma ray absorption method. However, the signals received from radiation detectors contain a significant stochastic noise, which makes them difficult to analyse. The article describes four methods of noise reduction in cross-correlation measurements of water-air...
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Hybrid Processing by Turning and Burnishing of Machine Components
PublikacjaThe paper presents a method of hybrid manufacturing process of long 5 shafts and deep holes by simultaneous turning and burnishing method. The tech- 6 nological results of the research focus on the influence of the basic technological 7 parameters of this process on the surface roughness of piston rods of hydraulic 8 cylinders. Research results are presented in the graphs as well as mathematical 9 formula. Set of samples were made...
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Bounds on the cover time of parallel rotor walks
PublikacjaThe rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, a set of k identical walkers is deployed in parallel, starting from a chosen subset of nodes, and moving around the graph in synchronous steps. During the process, each node successively propagates walkers visiting it along its outgoing arcs in round-robin fashion, according to a fixed ordering. We consider...
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Problems of Measuring Gas Content in Oil in a Two-Phase Flow: A Review
PublikacjaIn view of the necessity of measuring the air content in oil in two-phase flows in the context of general industry, a review of the most popular methods of measuring the air content in oil was carried out. This review includes an assessment of their advantages and disadvantages and of whether they meet criteria such as the degree of filling, the size and number of bubbles, verification, the absence of additional pressure drops,...
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Experimental Studies of Concrete-Filled Composite Tubes under Axial Short- and Long-Term Loads
PublikacjaThe paper presents experimental studies on axially compressed columns made of concrete-filled glass fiber reinforced polymer (GFRP) tubes. The infill concrete was C30/37 according to Eurocode 2. The investigated composite pipes were characterized by different angles of fiber winding in relation to the longitudinal axis of the element: 20, 55 and 85 degrees. Columns of two lengths, 0.4 m and 2.0 m, were studied. The internal diameter...
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GRAPHS AND COMBINATORICS
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Bounds on the Cover Time of Parallel Rotor Walks
PublikacjaThe rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, a set of k identical walkers is deployed in parallel, starting from a chosen subset of nodes, and moving around the graph in synchronous steps. During the process, each node maintains a cyclic ordering of its outgoing arcs, and successively propagates walkers which visit it along its outgoing arcs in...
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Dynamic F-free Coloring of Graphs
PublikacjaA problem of graph F-free coloring consists in partitioning the vertex set of a graph such that none of the resulting sets induces a graph containing a fixed graph F as an induced subgraph. In this paper we consider dynamic F-free coloring in which, similarly as in online coloring, the graph to be colored is not known in advance; it is gradually revealed to the coloring algorithm that has to color each vertex upon request as well...
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Dissecting gamma frequency activities during human memory processing
PublikacjaGamma frequency activity (30-150 Hz) is induced in cognitive tasks and is thought to reflect underlying neural processes. Gamma frequency activity can be recorded directly from the human brain using intracranial electrodes implanted in patients undergoing treatment for drug-resistant epilepsy. Previous studies have independently explored narrowband oscillations in the local field potential and broadband power increases. It is not...
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Gamma oscillations precede interictal epileptiform spikes in the seizure onset zone
PublikacjaOBJECTIVE: To investigate the generation, spectral characteristics, and potential clinical significance of brain activity preceding interictal epileptiform spike discharges (IEDs) recorded with intracranial EEG. METHODS: Seventeen adult patients with drug-resistant temporal lobe epilepsy were implanted with intracranial electrodes as part of their evaluation for epilepsy surgery. IEDs detected on clinical macro- and research microelectrodes...
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Wartości współczynnika N-gamma uzyskane z badań modelowych.
PublikacjaW artykule przedstawiono wyniki badań modelowych nośności jednorodnego podłoża gruntowego ograniczonego warstwą nieodkształcalną i obciążonego fundamentem pasmowym. Wyznaczono wartości współczynnika nośności N-gamma oraz skorygowanego N-gamma, prim, które porównano z istniejącym rozwiązaniem teoretycznym Mandela i Salencona.
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Strategic balance in graphs
PublikacjaFor a given graph G, a nonempty subset S contained in V ( G ) is an alliance iff for each vertex v ∈ S there are at least as many vertices from the closed neighbourhood of v in S as in V ( G ) − S. An alliance is global if it is also a dominating set of G. The alliance partition number of G was defined in Hedetniemi et al. (2004) to be the maximum number of sets in a partition of V ( G ) such that each set is an alliance. Similarly,...
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Dynamic coloring of graphs
PublikacjaDynamics is an inherent feature of many real life systems so it is natural to define and investigate the properties of models that reflect their dynamic nature. Dynamic graph colorings can be naturally applied in system modeling, e.g. for scheduling threads of parallel programs, time sharing in wireless networks, session scheduling in high-speed LAN's, channel assignment in WDM optical networks as well as traffic scheduling. In...
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Some variations of perfect graphs
PublikacjaWe consider (ψk−γk−1)-perfect graphs, i.e., graphs G for which ψk(H) =γk−1(H) for any induced subgraph H of G, where ψk and γk−1 are the k -path vertex cover number and the distance (k−1)-domination number, respectively. We study (ψk−γk−1)-perfect paths, cycles and complete graphs for k≥2. Moreover, we provide a complete characterisation of (ψ2−γ1)-perfect graphs describing the set of its forbidden induced subgraphs and providing...
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Independent Domination Subdivision in Graphs
PublikacjaA set $S$ of vertices in a graph $G$ is a dominating set if every vertex not in $S$ is adjacent to a vertex in~$S$. If, in addition, $S$ is an independent set, then $S$ is an independent dominating set. The independent domination number $i(G)$ of $G$ is the minimum cardinality of an independent dominating set in $G$. The independent domination subdivision number $\sdi(G)$ is the minimum number of edges that must be subdivided (each...
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Double bondage in graphs
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G=(V,E) 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, denoted by gamma_d(G), is the minimum cardinality of a double dominating set of G. The double bondage number of G, denoted by b_d(G), is the minimum cardinality among all sets...
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Interval incidence coloring of bipartite graphs
PublikacjaIn this paper we study the problem of interval incidence coloring of bipartite graphs. We show the upper bound for interval incidence coloring number (χii) for bipartite graphs χii≤2Δ, and we prove that χii=2Δ holds for regular bipartite graphs. We solve this problem for subcubic bipartite graphs, i.e. we fully characterize the subcubic graphs that admit 4, 5 or 6 coloring, and we construct a linear time exact algorithm for subcubic...
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Apparent molar volumes and compressibilities of electrolytes and ions in gamma-butyrolactone
PublikacjaW oparciu o zmierzone wartości gęstości roztworów i rozpuszczalnika w temperaturach od 15 do 40oC wyznaczono pozorne molowe objętości bromku litu, nadchloranu litu, nadchloranu sodu, tetrafenyloboranu sodu oraz bromku tetrafenylofosfoniowego w gamma-butyrolaktonie. Ponadto, wyznaczone prędkości rozchodzenia się dźwięku w 25oC w badanych układach pozwoliły obliczyć pozorne molowe ściśliwości wybranej grupy soli. Uzyskane (w wyniku...
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Global edge alliances in graphs
PublikacjaIn the paper we introduce and study a new problem of finding a minimum global edge alliance in a graph which is related to the global defensive alliance (Haynes et al., 2013; Hedetniemi, 2004) and the global defensive set (Lewoń et al., 2016). We proved the NP-completeness of the global edge alliance problem for subcubic graphs and we constructed polynomial time algorithms for trees. We found the exact values of the size of the...
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Review of Diameter protocol implementations for realization of communication in NGN networks
PublikacjaIn the paper Diameter protocol as well as its applications in the context of Next Generation Network (NGN) are described. Diameter message content and Attribute-Value Pairs (AVPs) concept are presented. Critical review of open source Diameter implementations is carried out. The performed analysis takes into consideration programming language, availability, support and documentation aspects. Basing on the review project fulfilling...
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Some Progress on Total Bondage in Graphs
PublikacjaThe total bondage number b_t(G) of a graph G with no isolated vertex is the cardinality of a smallest set of edges E'⊆E(G) for which (1) G−E' has no isolated vertex, and (2) γ_t(G−E')>γ_t(G). We improve some results on the total bondage number of a graph and give a constructive characterization of a certain class of trees achieving the upper bound on the total bondage number.
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Algorithms for testing security in graphs
PublikacjaIn this paper we propose new algorithmic methods giving with the high probability the correct answer to the decision problem of security in graphs. For a given graph G and a subset S of a vertex set of G we have to decide whether S is secure, i.e. every subset X of S fulfils the condition: |N[X] \cap S| >= |N[X] \ S|, where N[X] is a closed neighbourhood of X in graph G. We constructed a polynomial time property pseudotester based...
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Evaluation of the structures size in the liquid-gas flow by gamma-ray absorption
PublikacjaThe rapid development of tomography methods particularly electrical, X and gamma rays allows for a wide range of the information about flow structure. However, all of such methods are quite complicated. At the same time much simpler systems as the measuring system of gamma rays absorption, allows to obtain a all key flow information which describe the two-phase flow. In the article the results of analyzes of radiometric signal...
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2-bondage in graphs
PublikacjaA 2-dominating set of a graph G=(V,E) is a set D of vertices of G such that every vertex of V(G)D has at least two neighbors in D. The 2-domination number of a graph G, denoted by gamma_2(G), is the minimum cardinality of a 2-dominating set of G. The 2-bondage number of G, denoted by b_2(G), is the minimum cardinality among all sets of edges E' subseteq E such that gamma_2(G-E') > gamma_2(G). If for every E' subseteq E we have...
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The effect of circular saw blade clamping diameter on its resonant frequencies
PublikacjaIn this paper results of comparison of characteristic resonant frequencies of circular saw blades as a function of saw clamping diameter from the impact test are presented. Obtained results revealed that proportionally with the increase of the saw clamping diameter also the dynamical stiffness of the saw blade increased. As a consequence of that the resonant frequencies of the saw blade move to higher values. Moreover, with the...
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The Effect of Circular Saw Blade Clamping Diameter on its Resonant Frequencies
PublikacjaIn this paper results of comparison of characteristic resonant frequencies of circular saw blades as a function of the saw clamping diameter from the impact test are presented. Obtained results revealed that proportionally with the increase of the saw clamping diameter also the dynamical stiffness of the saw blade increased. As a consequence of that the resonant frequencies of the saw blade move to higher values. Moreover, with...
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On-line P-coloring of graphs
PublikacjaFor a given induced hereditary property P, a P-coloring of a graph G is an assignment of one color to each vertex such that the subgraphs induced by each of the color classes have property P. We consider the effectiveness of on-line P-coloring algorithms and give the generalizations and extensions of selected results known for on-line proper coloring algorithms. We prove a linear lower bound for the performance guarantee function...
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A note on total reinforcement in graphs
PublikacjaIn this note we prove a conjecture and inprove some results presendet in a recent paper of N. Sridharan, M.D. Elias, V.S.A. Subramanian, Total reinforcement number of a graph, AKCE Int. J. Graphs Comb. 4 (2) (2007) 197-202.
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Serwer Diameter w architekturze Proxy Mobile IPv6
PublikacjaW pracy przedstawiono mechanizmy współpracy serwera Diameter z systemem Proxy Mobile IPv6. Opisany został sposób integracji obu rozwiązań na potrzeby obsługi mobilności terminali ruchomych w sieci IPv6. W ramach realizowanych badań wykonano implementację opisanego systemu. Dla przygotowanej implementacji przeprowadzono szereg testów wydajnościowych uwzględniających parametry jakości QoS oraz QoE.
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On the metric dimension of corona product graphs
PublikacjaWe give several results on the metric dimension of corona product graphs.
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Edge and Pair Queries-Random Graphs and Complexity
PublikacjaWe investigate two types of query games played on a graph, pair queries and edge queries. We concentrate on investigating the two associated graph parameters for binomial random graphs, and showing that determining any of the two parameters is NP-hard for bounded degree graphs.
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Computational aspects of greedy partitioning of graphs
PublikacjaIn this paper we consider a variant of graph partitioning consisting in partitioning the vertex set of a graph into the minimum number of sets such that each of them induces a graph in hereditary class of graphs P (the problem is also known as P-coloring). We focus on the computational complexity of several problems related to greedy partitioning. In particular, we show that given a graph G and an integer k deciding if the greedy...
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Colorings of the Strong Product of Circulant Graphs
PublikacjaGraph coloring is one of the famous problems in graph theory and it has many applications to information theory. In the paper we present colorings of the strong product of several circulant graphs.
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Bondage number of grid graphs
PublikacjaThe 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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2-outer-independent domination in graphs
PublikacjaWe initiate the study of 2-outer-independent domination in graphs. A 2-outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)\D has at least two neighbors in D, and the set V(G)\D is independent. The 2-outer-independent domination number of a graph G is the minimum cardinality of a 2-outer-independent dominating set of G. We show that if a graph has minimum degree at least two,...
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Theory and Applications of Graphs
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Edge coloring of graphs of signed class 1 and 2
PublikacjaRecently, Behr (2020) introduced a notion of the chromatic index of signed graphs and proved that for every signed graph (G, σ) it holds that ∆(G) ≤ χ′(G,σ) ≤ ∆(G) + 1, where ∆(G) is the maximum degree of G and χ′ denotes its chromatic index. In general, the chromatic index of (G, σ) depends on both the underlying graph G and the signature σ. In the paper we study graphs G for which χ′(G, σ) does not depend on σ. To this aim we...
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The hat problem on a union of disjoint graphs
PublikacjaThe topic is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of winning. In this version every player...
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On the super domination number of lexicographic product graphs
PublikacjaThe 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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Common Independence in Graphs
PublikacjaAbstract: The cardinality of a largest independent set of G, denoted by α(G), is called the independence number of G. The independent domination number i(G) of a graph G is the cardinality of a smallest independent dominating set of G. We introduce the concept of the common independence number of a graph G, denoted by αc(G), as the greatest integer r such that every vertex of G belongs to some independent subset X of VG with |X|...
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Direct electrical stimulation of the human brain has inverse effects on the theta and gamma neural activities
PublikacjaObjective: Our goal was to analyze the electrophysiological response to direct electrical stimulation (DES) systematically applied at a wide range of parameters and anatomical sites, with particular focus on neural activities associated with memory and cognition. Methods: We used a large set of intracranial EEG (iEEG) recordings with DES from 45 subjects with electrodes...
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Deterministic Rendezvous in Restricted Graphs
PublikacjaIn this paper we consider the problem of synchronous rendezvous in which two anonymous mobile entities (robots) A and B are expected to meet at the same time and point in a graph G = (V;E). Most of the work devoted to rendezvous in graphs assumes that robots have access to the same sets of nodes and edges, where the topology of connections may be initially known or unknown. In our work we assume the movement of robots is restricted...
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Burnout Investigation of Small Diameter Tubes Immersed in Nanofluids
PublikacjaThis paper deals with research into pool boiling critical heat flux (CHF) of water–Al2O3, water–TiO2 and water–Cu nanofluids on horizontal stainless steel tubes. The experiments were conducted under atmospheric pressure. Nanoparticles were tested at concentrations of 0.001%, 0.01%, 0.1% and 1% by weight. Ultrasonic vibration was used in order to stabilize the dispersion of the nanoparticles. Although dispersants were not used to...
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Three-fast-searchable graphs
PublikacjaIn the edge searching problem, searchers move from vertex to vertex in a graph to capture an invisible, fast intruder that may occupy either vertices or edges. Fast searching is a monotonic internal model in which, at every move, a new edge of the graph G must be guaranteed to be free of the intruder. That is, once all searchers are placed the graph G is cleared in exactly |E(G)| moves. Such a restriction obviously necessitates...
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On bipartization of cubic graphs by removal of an independent set
PublikacjaWe study a new problem for cubic graphs: bipartization of a cubic graph Q by deleting sufficiently large independent set.