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Search results for: STRUCTURAL POUNDIN G
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An upper bound on the total outer-independent domination number of a tree
PublicationA total outer-independent dominating set of a graph G=(V(G),E(G)) is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V(G)D is independent. The total outer-independent domination number of a graph G, denoted by gamma_t^{oi}(G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every tree T of order n >= 4, with l leaves and s support vertices we have...
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On the ratio between 2-domination and total outer-independent domination numbers of trees
PublicationA 2-dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)D has a at least two neighbors in D. A total outer-independent 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, and the set V(G)D is independent. The 2-domination (total outer-independent domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (total...
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Block graphs with large paired domination multisubdivision number
PublicationThe paired domination multisubdivision number of a nonempty graph G, denoted by msdpr(G), is the smallest positive integer k such that there exists an edge which must be subdivided k times to increase the paired domination number of G. It is known that msdpr(G) ≤ 4 for all graphs G. We characterize block graphs with msdpr(G) = 4.
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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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New potential functions for greedy independence and coloring
PublicationA potential function $f_G$ of a finite, simple and undirected graph $G=(V,E)$ is an arbitrary function $f_G : V(G) \rightarrow \mathbb{N}_0$ that assigns a nonnegative integer to every vertex of a graph $G$. In this paper we define the iterative process of computing the step potential function $q_G$ such that $q_G(v)\leq d_G(v)$ for all $v\in V(G)$. We use this function in the development of new Caro-Wei-type and Brooks-type...
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Obtaining and Characterization of the PLA/Chitosan Foams with Antimicrobial Properties Achieved by the Emulsification Combined with the Dissolution of Chitosan by CO2 Saturation
PublicationA new method of obtaining functional foam material has been proposed. The materials were created by mixing the poly lactic acid (PLA) solution in chloroform, chitosan (CS) dissolved in water saturated with CO2 and polyethylene glycol (PEG), and freeze-dried for removal of the solvents. The composite foams were characterized for their structural (SEM, FT-IR, density, porosity), thermal (DSC), functional (hardness, elasticity, swelling...
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Obtaining and Characterization of the PLA/Chitosan Foams with Antimicrobial Properties Achieved by the Emulsification Combined with the Dissolution of Chitosan by CO2 Saturation
PublicationA new method of obtaining functional foam material has been proposed. The materials were created by mixing the poly lactic acid (PLA) solution in chloroform, chitosan (CS) dissolved in water saturated with CO2 and polyethylene glycol (PEG), and freeze-dried for removal of the solvents. The composite foams were characterized for their structural (SEM, FT-IR, density, porosity), thermal (DSC), functional (hardness, elasticity, swelling...
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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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Structural motifs in the Cu(II), Mn(II) and Zn(II) complexes based on N,N,N-donor dipodal or N,N,N,N-donor tripodal ligands obtained in situ: Synthesis, crystal structures and xanthine oxidase inhibition properties
PublicationA series of four novel transition metal complexes, [Cu(NCS)2L1] (1), [Mn(NCS)2L1] (2) where L1 = bis(1-(3,5-dimethylpyrazolyl)methyl)amine, [Mn(NCS)2L2] (3) and [Zn(NCS)L2]2[Zn(NCS)4] (4) where L2 = tris(1-(3,5-dimethylpyrazolyl)methyl)amine, has been obtained in situ by a one-step, one-pot synthetic path starting from 1-hydroxymethyl-3,5-dimethylpyrazole (L). The isolated complexes were fully characterised by elemental analysis,...
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The influence of the type of halogen substituent and its position on the molecular conformation, intermolecular interactions and crystal packing for a series of 1-benzoyl-3-(halogenophenyl)thioureas
PublicationBy the reaction of benzoyl chloride, potassium isothiocyanate and the appropriate halogenoaniline, i.e. 2/3/4-(bromo/iodo)aniline, we have obtained five new 1-benzoyl-3-(halogenophenyl)thioureas, namely, 1-benzoyl-3-(2-bromophenyl)- thiourea and 1-benzoyl-3-(3-bromophenyl)thiourea, C14H11BrN2OS, and 1-benzoyl-3-(2-iodophenyl)thiourea, 1-benzoyl-3-(3-iodophenyl)thiourea and 1-benzoyl-3-(4-iodophenyl)thiourea, C14H11IN2OS. Structural...
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On the size of identifying codes in triangle-free graphs
PublicationIn an undirected graph G, a subset C⊆V(G) such that C is a dominating set of G, and each vertex in V(G) is dominated by a distinct subset of vertices from C, is called an identifying code of G. The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. For a given identifiable graph G, let gammaID(G) be the minimum cardinality of an identifying code in G. In this paper, we show that for any connected...
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Minimum order of graphs with given coloring parameters
PublicationA complete k-coloring of a graph G=(V,E) is an assignment F: V -> {1,...,k} of colors to the vertices such that no two vertices of the same color are adjacent, and the union of any two color classes contains at least one edge. Three extensively investigated graph invariants related to complete colorings are the minimum and maximum number of colors in a complete coloring (chromatic number χ(G) and achromatic number ψ(G), respectively),...
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Laser Induced Piezo-Optical Effects in Chalcogenides
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Some Progress on Total Bondage in Graphs
PublicationThe 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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An analysis of the prevalence of thyroid autoantibodies: thyroid peroxidase antibodies (ATA) and thyroglobulin antibodies (ATG) in children with newly diagnosed diabetes mellitus type 1 during 2000–2004 in the Upper Silesia region, Poland
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Action of an Antiserum to a-Tocoquinone on Photosystem II-Particle Preparations of N icotiana tabacum
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Dielectric and electro-optic studies of a bimesogenic liquid crystal composed of bent-core and calamitic units
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Augmentation index, pulse pressure amplification and superoxide anion production in patients with coronary artery disease
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2007 Guidelines for the management of arterial hypertension: The Task Force for the Management of Arterial Hypertension of the European Society of Hypertension (ESH) and of the European Society of Cardiology (ESC)
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A lower bound on the total outer-independent domination number of a tree
PublicationA total outer-independent 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, and the set V(G)D is independent. The total outer-independent domination number of a graph G, denoted by gamma_t^{oi}(G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every nontrivial tree T of order n with l leaves we have gamma_t^{oi}(T) >= (2n-2l+2)/3,...
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On trees with equal domination and total outer-independent domination numbers
PublicationFor a graph G=(V,E), a subset D subseteq V(G) is a dominating set if every vertex of V(G)D has a neighbor in D, while it is a total outer-independent dominating set if every vertex of G has a neighbor in D, and the set V(G)D is independent. The domination (total outer-independent domination, respectively) number of G is the minimum cardinality of a dominating (total outer-independent dominating, respectively) set of G. We characterize...
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GreedyMAX-type Algorithms for the Maximum Independent Set Problem
PublicationA maximum independent set problem for a simple graph G = (V,E) is to find the largest subset of pairwise nonadjacent vertices. The problem is known to be NP-hard and it is also hard to approximate. Within this article we introduce a non-negative integer valued functionp defined on the vertex set V(G) and called a potential function of agraph G, while P(G) = max{vinV(G)| p(v)} is called a potential of G. For any graph P(G) <= D(G),...
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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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An upper bound on the 2-outer-independent domination number of a tree
PublicationA 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 a at least two neighbors in D, and the set V(G)D is independent. The 2-outer-independent domination number of a graph G, denoted by gamma_2^{oi}(G), is the minimum cardinality of a 2-outer-independent dominating set of G. We prove that for every nontrivial tree T of order n with l leaves we have gamma_2^{oi}(T) <= (n+l)/2,...
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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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Superhydrophobic and superoleophilic melamine sponges impregnated with deep eutectic solvents for oil spill cleanup
PublicationThe extensive extraction of oil from the bottom of seas and oceans and its transportation by tankers increase the risk of potential environmental disasters associated with hydrocarbon fractions entering water reservoirs. Therefore, this paper presents the preparation of a simple impregnation of a melamine sponge with deep eutectic solvents (DES), which can be obtained from natural sources, including coconut oil, palm kernel oil,...
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Parity vertex colouring of graphs
PublicationA 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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Equitable coloring of corona products of graphs
PublicationIn this paper we consider an equitable coloring of some corona products of graphs G and H in symbols, G o H). In particular, we show that deciding the colorability of G o H is NP-complete even if G is 4-regular and H is K_2. Next, we prove exact values or upper bounds on the equitable chromatic number of G o H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a path, a cycle or a complete graph.
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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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Bone status in adolescents with type 1 diabetes
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The Escherichia coli RNA polymerase alpha subunit and transcriptional activation by bacteriophage lambda CII protein.
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Graphs with isolation number equal to one third of the order
PublicationA set D of vertices of a graph G is isolating if the set of vertices not in D and with no neighbor in D is independent. The isolation number of G, denoted by \iota(G) , is the minimum cardinality of an isolating set of G. It is known that \iota(G) \leq n/3 , if G is a connected graph of order n, , distinct from C_5 . The main result of this work is the characterisation of unicyclic and block graphs of order n with isolating number...
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Low frequency noise and reliability properties of 0.12um CMOS devices with Ta2O5 as gate dielectrics
PublicationW artykule przedstawiono wyniki badań jakości tranzystorów CMOS 0.12um z Ta2O5 użytym jako dielektryk bramki. Przedstawione są charakterystyki statyczne elementów oraz wyniki pomiarów szumów prowadzonych w celu określenia jakości warstwy dielektrycznej Ta2O5, a także wyniki badań przeciążeniowych elementów.
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Carbon Nanotubes Chemically Derivatized with Redox Systems as Mediators for Biofuel Cell Applications
PublicationEnzymatyczne bioogniwa paliwowe to urządzenia wykorzystujące enzymy do przemiany energii chemicznej w elektryczną. Zyskana w ten sposób energia może służyć do zasilania wszczepialnych urządzeń (np. czujników glukozy, rozruszników serca). Przedstawiono sposób otrzymywania i właściwości bioelektrod, w których wykorzystano nanorurki węglowe modyfikowane mediatorami enzymatycznych reakcji redoks. Do nanorurek przyłączano zarówno mediatory...
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Occurrence, contamination evaluation and health risks of trace metals within soil, sediments and tailings in southern Tunisia
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SU‐E‐T‐103: Three‐Dimensional Measurements of Dose and LET from a Proton Beam via Polymer Gel Dosimetry
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Magnetic resonance imaging of radiation dose distributions using a polymer-gel dosimeter
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Ecological trends in machining as a key factor in sustainable production – A review
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Vehicular Communication Environments
PublicationCommunication to and between road vehicles (cars, truck, buses, trains, etc.) are of growing interest. This is partly due to the attractive services that cooperative intelligent transport systems (C-ITSs) provides, mainly in the areas of traffic safety and traffic efficiency. An enabler for C-ITS is wireless vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication, collectively referred to as vehicle-to-X (V2X)...
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RDF dataset profiling - a survey of features, methods, vocabularies and applications
PublicationThe Web of Data, and in particular Linked Data, has seen tremendous growth over the past years. However, reuse and take-up of these rich data sources is often limited and focused on a few well-known and established RDF datasets. This can be partially attributed to the lack of reliable and up-to-date information about the characteristics of available datasets. While RDF datasets vary heavily with respect to the features related...
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Engineering Au nanoparticle arrays on SiO2 glass by pulsed UV laser irradiation
PublicationWe study semi-regular arrays of Au nanoparticles (NP) obtained via UV laser irradiation of thin Au films on glass substrate. The NP structures are prepared from films of a thickness up to 60 nm produced by discharge sputtering or pulsed laser deposition, and annealed by nanosecond laser pulses at 266 or 308 nm, respectively, at fluencies in the range of 60-410 mJ/cm2. For the rare- and close-packed NP structures, consistent description...
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The Backbone Coloring Problem for Bipartite Backbones
PublicationLet G be a simple graph, H be its spanning subgraph and λ≥2 be an integer. By a λ -backbone coloring of G with backbone H we mean any function c that assigns positive integers to vertices of G in such a way that |c(u)−c(v)|≥1 for each edge uv∈E(G) and |c(u)−c(v)|≥λ for each edge uv∈E(H) . The λ -backbone chromatic number BBCλ(G,H) is the smallest integer k such that there exists a λ -backbone coloring c of G with backbone H satisfying...
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Review of cigars and cigar-type products as potential sources of consumer exposure to heavy metals
PublicationThe popularity of cigars, growing since 1993, has not gone hand in hand with the increased interest of researchers in these products. Although the literature widely describes the harmfulness of tobacco and the content of toxic substances in tobacco products, the topic is often treated selectively as relating primarily to cigarettes and rarely extends to other products of the broadly defined tobacco industry. However, there is no...
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An upper bound for the double outer-independent domination number of a tree
PublicationA vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent 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, and the set V(G)\D is independent. The double outer-independent domination number of a graph G, denoted by γ_d^{oi}(G), is the minimum cardinality of a double outer-independent dominating set of G. We prove...
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Impact of aeration conditions on the removal of low concentrations of nitrogen in a tertiary partially aerated biological filter
PublicationA submerged biological aerated filter (BAF) partially aerated was used to study the removal of low concentrations of ammonia nitrogen (0.3 g N/m3 to 30.5 g N/m3) typically found in nutrient enriched river and lake waters, and treated effluents. Four series of experiments were performed with a synthetic wastewater at ammonia loading rates between 6 g N/m3 d and 903 g N/m3 d and C/N ratios from 2 to 20. The results showed that ammonia...
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BTEX concentration levels in urban air in the area of the Tri-City agglomeration (Gdansk, Gdynia, Sopot), Poland
PublicationThe paper presents and discusses the results of atmospheric air quality research conducted in 2012 with reference to the level of BTEX compounds in the Tri-City agglomeration—Gdansk, Gdynia, and Sopot (northern Poland). At the stage of BTEX sampling from the ambient air, Radiello® diffusive passive samplers were applied. The annual time-weighted average concentrations for benzene, toluene, ethylbenzene, and xylenes (BTEX) in the...
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Progress on Roman and Weakly Connected Roman Graphs
PublicationA graph G for which γR(G)=2γ(G) is the Roman graph, and if γwcR(G)=2γwc(G), then G is the weakly connected Roman graph. In this paper, we show that the decision problem of whether a bipartite graph is Roman is a co-NP-hard problem. Next, we prove similar results for weakly connected Roman graphs. We also study Roman trees improving the result of M.A. Henning’s A characterization of Roman trees, Discuss. Math. Graph Theory 22 (2002)....
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On trees with equal 2-domination and 2-outer-independent domination numbers
PublicationFor 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 in D, while it is a 2-outer-independent dominating set if additionally the set V(G)\D is independent. The 2-domination (2-outer-independent domination, respectively) number of G, is the minimum cardinality of a 2-dominating (2-outer-independent dominating, respectively) set of G. We characterize all trees...
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A Noether theorem for stochastic operators on Schatten classes
PublicationWe prove that a stochastic (Markov) operator S acting on a Schatten class C_1 satisfies the Noether condition S'(A) = A and S'(A^2) = A^2, where A is a Hermitian bounded linear operator on a complex Hilbert space H, if and only if, S(E(G)XE(G)) = E(G)S(X)E(G) holds true for every Borel subset G of the real line R, where E(G) denotes the orthogonal projection coming from the spectral resolution of A. Similar results are obtained...
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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublicationConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...