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Search results for: SHANNON CAPACITY OF GRAPHS
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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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THE SCIENTIFIC CAPACITY AS AN INNOVATION DETERMINANT OF THE POLISH REGIONS
PublicationEvery Polish region (in the paper understood as a voivodship) is an inspiring ground for comparative studies on the national as well as European scale, i.e. with regard to the administrative units of the other European countries. The aim of the article is to advance the conclusions concerning the Regional Innovation Scoreboard – a European instrument applied to examine the innovation capacity of European regions – with the issues...
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Paired domination subdivision and multisubdivision numbers of graphs
PublicationThe paired domination subdivision number sdpr(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the paired domination number of G. We prove that the decision problem of the paired domination subdivision number is NP-complete even for bipartite graphs. For this reason we define the paired domination muttisubdivision number of a nonempty graph...
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Domination subdivision and domination multisubdivision numbers of graphs
PublicationThe domination subdivision number sd(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the domination number of G. It has been shown [10] that sd(T)<=3 for any tree T. We prove that the decision problem of the domination subdivision number is NP-complete even for bipartite graphs. For this reason we define the domination multisubdivision number...
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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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An Approximation of the Zero Error Capacity by a Greedy Algorithm
PublicationWe present a greedy algorithm that determines a lower bound on the zero error capacity. The algorithm has many new advantages, e.g., it does not store a whole product graph in a computer memory and it uses the so-called distributions in all dimensions to get a better approximation of the zero error capacity. We also show an additional application of our algorithm.
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An Approximation of the Zero Error Capacity by a Greedy Algorithm.
PublicationWe present a greedy algorithm that determines a lower bound on the zero error capacity. The algorithm has many new advantages, e.g., it does not store a whole product graph in a computer memory and it uses the so-called distributions in all dimensions to get a better approximation of the zero error capacity. We also show an additional application of our algorithm.
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Equitable colorings of some variation of corona products of cubic graphs
PublicationThe problem of determining the value of equitable chromatic number for multicoronas of cubic graphs is studied. We provide some polynomially solvable cases of cubical multicoronas and give simple linear time algorithms for equitable coloring of such graphs which use almost optimal number of colors in the remaining cases.
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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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Cops, a fast robber and defensive domination on interval graphs
PublicationThe game of Cops and ∞-fast Robber is played by two players, one controlling c cops, the other one robber. The players alternate in turns: all the cops move at once to distance at most one each, the robber moves along any cop-free path. Cops win by sharing a vertex with the robber, the robber by avoiding capture indefinitely. The game was proposed with bounded robber speed by Fomin et al. in “Pursuing a fast robber on a graph”,...
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The paired-domination and the upper paired-domination numbers of graphs
PublicationIn this paper we obtain the upper bound for the upper paired-domination number and we determine the extremal graphs achieving this bound. Moreover we determine the upper paired- domination number for cycles.
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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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All graphs with paired-domination number two less than their order
PublicationLet G=(V,E) be a graph with no isolated vertices. A set S⊆V is a paired-dominating set of G if every vertex not in S is adjacent with some vertex in S and the subgraph induced by S contains a perfect matching. The paired-domination number γp(G) of G is defined to be the minimum cardinality of a paired-dominating set of G. Let G be a graph of order n. In [Paired-domination in graphs, Networks 32 (1998), 199-206] Haynes and Slater...
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Domination-Related Parameters in Rooted Product Graphs
PublicationAbstract A set S of vertices of a graph G is a dominating set in G if every vertex outside of S is adjacent to at least one vertex belonging to S. A domination parameter of G is related to those sets of vertices of a graph satisfying some domination property together with other conditions on the vertices of G. Here, we investigate several domination-related parameters in rooted product graphs.
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The Energy of Finance in Refining of Medical Surge Capacity
PublicationThe availability of resources and their concentration in the place of greatest need, will not allow us to successfully overcome a medical surge without the energy required to activate these resources and activities, and increase their quantities if necessary, that is why the staff and management of healthcare institutions are forced to making ethical crisis decisions about who wins and who loses. This study highlights the versatility...
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Secure Italian domination in graphs
PublicationAn Italian dominating function (IDF) on a graph G is a function f:V(G)→{0,1,2} such that for every vertex v with f(v)=0, the total weight of f assigned to the neighbours of v is at least two, i.e., ∑u∈NG(v)f(u)≥2. For any function f:V(G)→{0,1,2} and any pair of adjacent vertices with f(v)=0 and u with f(u)>0, the function fu→v is defined by fu→v(v)=1, fu→v(u)=f(u)−1 and fu→v(x)=f(x) whenever x∈V(G)∖{u,v}. A secure Italian dominating...
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Eqiuitable coloring of corona products of cubic graphs is harder than ordinary coloring
PublicationA graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G. In this paper the problem of determinig the equitable coloring number for coronas of cubic graphs is studied. Although the problem of ordinary coloring of coronas...
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Synchronous black hole search in directed graphs
PublicationThe paper considers a team of robots which has to explore a graph G, where some nodes can be harmful. Robots are initially located at the so-called home base node. The dangerous nodes are the so-called black hole nodes, and once a robot enters in one of them, it is destroyed. The goal is to find a strategy in order to explore G in such a way that minimum number of robots is wasted. The exploration ends if there is at least one...
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Interval Edge Coloring of Bipartite Graphs with Small Vertex Degrees
PublicationAn edge coloring of a graph G is called interval edge coloring if for each v ∈ V(G) the set of colors on edges incident to v forms an interval of integers. A graph G is interval colorable if there is an interval coloring of G. For an interval colorable graph G, by the interval chromatic index of G, denoted by χ'_i(G), we mean the smallest number k such that G is interval colorable with k colors. A bipartite graph G is called (α,β)-biregular...
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The computational complexity of the backbone coloring problem for planar graphs with connected backbones
PublicationIn the paper we study the computational complexity of the backbone coloring problem for planar graphs with connected backbones. For every possible value of integer parameters λ≥2 and k≥1 we show that the following problem: Instance: A simple planar graph GG, its connected spanning subgraph (backbone) HH. Question: Is there a λ-backbone coloring c of G with backbone H such that maxc(V(G))≤k? is either NP-complete or polynomially...
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INFLUENCE OF TIME ON THE BEARING CAPACITY OF PRECAST PILES
PublicationOne of the most popular types of foundations in layered subsoil with very differentiated soil shear strengths are precast piles. One of the reasons is a fact that we can well control the driving process during the installation of these piles. The principles of the assessment of bearing capacity and settlements of the piles given by Eurocode 7, concentrate on two main methods, i.e. Static Pile Load Tests (SPLT) and Dynamic Driving...
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On Symmetry of Uniform and Preferential Attachment Graphs
PublicationMotivated by the problem of graph structure compression under realistic source models, we study the symmetry behavior of preferential and uniform attachment graphs. These are two dynamic models of network growth in which new nodes attach to a constant number m of existing ones according to some attachment scheme. We prove symmetry results for m=1 and 2 , and we conjecture that for m≥3 , both models yield asymmetry with high...
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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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Equitable coloring of graphs. Recent theoretical results and new practical algorithms
PublicationIn this paper we survey recent theoretical results concerning conditions for equitable colorability of some graphs and recent theoretical results concerning the complexity of equitable coloring problem. Next, since the general coloring problem is strongly NP-hard, we report on practical experiments with some efficient polynomial-time algorithms for approximate equitable coloring of general graphs.
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Approximation algorithms for job scheduling with block-type conflict graphs
PublicationThe problem of scheduling jobs on parallel machines (identical, uniform, or unrelated), under incompatibility relation modeled as a block graph, under the makespan optimality criterion, is considered in this paper. No two jobs that are in the relation (equivalently in the same block) may be scheduled on the same machine in this model. The presented model stems from a well-established line of research combining scheduling theory...
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Average distance is submultiplicative and subadditive with respect to the strong product of graphs
PublicationWe show that the average distance is submultiplicative and subadditive on the set of non-trivial connected graphs with respect to the strong product. We also give an application of the above-mentioned result.
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On incidence coloring of coloring of complete multipartite and semicubic bipartite graphs
PublicationIn the paper, we show that the incidence chromatic number of a complete k-partite graph is at most ∆+2 (i.e., proving the incidence coloring conjecture for these graphs) and it is equal to ∆+1 if and only if the smallest part has only one vertex.
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A simple test for quantum channel capacity
PublicationBased on state and channel isomorphism we point out that semidefiniteprogramming can be used as a quick test for nonzero one-way quantum channelcapacity. This can be achieved by searching for symmetric extensions of statesisomorphic to a given quantum channel. With this method we provide examplesof quantum channels that can lead to high entanglement transmission but stillhave zero one-way capacity, in particular, regions of symmetric...
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Towards Increasing Density of Relations in Category Graphs
PublicationIn the chapter we propose methods for identifying new associations between Wikipedia categories. The first method is based on Bag-of-Words (BOW) representation of Wikipedia articles. Using similarity of the articles belonging to different categories allows to calculate the information about categories similarity. The second method is based on average scores given to categories while categorizing documents by our dedicated score-based...
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Effect of Different Structure Type Traffic On Railway Line Capacity
PublicationThe article points to methods of analyzing railway traffic conditions based on two parameters: capacity and delay of trains. The impact of the differentiated railway type structure on the capacity of the railway line was presented. Particular attention has been paid to the assessment of commonly used simplifications in analyzes.
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Displacement piles - classification and methods for the calculation of bearing capacity.
PublicationDisplacement piles belong to a group of technologies whose main idea is to install or make a pile without extracting ground material. According to definition, contained in PN-EN:1997-1:2008, displacement piles should be considered as driven, pressed in using vibrators and made with the use of spread augers. The classification of piles used so far with regard to the technology of execution is modified. An additional element is the...
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The computational complexity of the backbone coloring problem for bounded-degree graphs with connected backbones
PublicationGiven a graph G, a spanning subgraph H of G and an integer λ>=2, a λ-backbone coloring of G with backbone H is a vertex coloring of G using colors 1, 2, ..., in which the color difference between vertices adjacent in H is greater than or equal to lambda. The backbone coloring problem is to find such a coloring with maximum color that does not exceed a given limit k. In this paper, we study the backbone coloring problem for bounded-degree...
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High load capacity spur gears with conchoidal path of contact
PublicationThe present study is devoted to investigation of spur gears with a conchoidal path of contact and a convex-convex contact between teeth. The load capacity and energy efficiency were evaluated using both theoretical and experimental approaches. The theoretical analysis showed that the conchoidal gear pairs are 5–21% stronger in terms of contact stress and have similar energy efficiency as compared to the involute gear pairs of the...
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Double ZIF-L structures with exceptional CO2 capacity
PublicationCarbon dioxide emission is an emerging problem nowadays and new methods are designed for its control. In this article, a report on the formation of zeolitic imidazole framework with an apparent double leaf-like morphology DZIF-L is given. The special structure of the materials prevents from aggregation of the particles providing remarkable CO2 capacity. At 0.1 MPa the CO2 uptake was 2.99 ± 0.06 mmol/g. The capacity of synthesized...
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Optimal backbone coloring of split graphs with matching backbones
PublicationFor a graph G with a given subgraph H, the backbone coloring is defined as the mapping c: V(G) -> N+ such that |c(u)-c(v)| >= 2 for each edge uv \in E(H) and |c(u)-c(v)| >= 1 for each edge uv \in E(G). The backbone chromatic number BBC(G;H) is the smallest integer k such that there exists a backbone coloring with max c(V(G)) = k. In this paper, we present the algorithm for the backbone coloring of split graphs with matching backbone.
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Scheduling on Uniform and Unrelated Machines with Bipartite Incompatibility Graphs
PublicationThe problem of scheduling jobs on parallel machines under an incompatibility relation is considered in this paper. In this model, a binary relation between jobs is given and no two jobs that are in the relation can be scheduled on the same machine. We consider job scheduling under the incompatibility relation modeled by a bipartite graph, under the makespan optimality criterion, on uniform and unrelated machines. Unrelated machines...
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Connection graphs
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Decontaminating Arbitrary Graphs by Mobile Agents: a Survey
PublicationA team of mobile agents starting from homebases need to visit and clean all nodes of the network. The goal is to find a strategy, which would be optimal in the sense of the number of needed entities, the number of moves performed by them or the completion time of the strategy. Currently, the field of distributed graph searching by a team of mobile agents is rapidly expanding and many new approaches and models are being presented...
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Bearing capacity of the working platform with kinematic method
PublicationBearing capacity of the working platform for heavy tracks was analysed using Distinct Layout Optimization (DLO) method. The platform layer constructed from cohesionless soils is resting on weak cohesive subgrade. Different thickness of the platform, its effective angle of internal friction and undrained shear strength of the soft soil were taken into consideration. Kinematic method permits different failure mechanisms to be analyzed....
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Capacity analysis of the selected track system in partially ordered space
PublicationA proper location of the interval sections has significant impact on the traffic flow in the railway track network. This issue is critical during line modernization as well as when a new solution accounting for the traffic forecast at particular element of the railway track network is developed . However, the situation is more complex and more expensive for railway stations since improvement of the capacity requires critical organizational...
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Axial capacity of steel built-up battened columns
PublicationThis paper deals with the numerical investigation aimed to study the axial capacity of pin-ended steel built-up columns. Three methods of calculating forces in chords and batten, taking into account the material and geometric imperfections specified in the Eurocode 3 are considered. The aim of this study was to compare different methods allowing the calculation of the column load capacity and determine a simpler and faster method...
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Development of the New Polish Method for Capacity Analysis of Motorways and Expressways
PublicationThe paper presents development of the new Polish method for performing capacity analysis of basic segments of dual carriageway roads (motorways and expressways). The method is based on field traffic surveys conducted at 30 motorway and expressway sites (class A and S roads) in Poland. Traffic flows, composition and travel times were observed in 15-min intervals at each site using ANPR filming method. These data were used to calibrate...
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A Framework for Searching in Graphs in the Presence of Errors
PublicationWe consider a problem of searching for an unknown target vertex t in a (possibly edge-weighted) graph. Each vertex-query points to a vertex v and the response either admits that v is the target or provides any neighbor s of v that lies on a shortest path from v to t. This model has been introduced for trees by Onak and Parys [FOCS 2006] and for general graphs by Emamjomeh-Zadeh et al. [STOC 2016]. In the latter, the authors provide...
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Towards rainfall interception capacity estimation using ALS LiDAR data
PublicationIn this study we develop a spatial model for interception capacity of vegetation based on LiDAR data. The study is conducted in the natural wetland river valley dominated meadows, reeds and small bushes. The multiple regression model was chosen to relate the field measurements of interception capacity and LiDAR statistics at 2m grid. The optimal model was chosen by stepwise selection and further manual variables selection resulting...
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Implementing Sustainable Development Goals with Digital Government – Aspiration-capacity gap
PublicationSustainable Development Goals (SDGs) represent a commitment by all United Nations Member States to pursue development efforts, including ending poverty and hunger, promoting well-being and education, reducing inequalities, fostering peace, and protecting the planet. Member States and their governments are supposed to take ownership of the SDGs, strengthen the implementation means, and improve public governance as both the means...
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An Efficient Noisy Binary Search in Graphs via Median Approximation
PublicationConsider 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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Numerical analysis on axial capacity of steel built-up battened columns
PublicationThis paper deals with the numerical analysis aimed at study the bearing capacity of pinended steel built-up columns under axial compression. Finite element (FE) models were performed for the columns presented in the literature. The main problem discussed in the article is the shape and magnitude of geometric imperfections introduced into the numerical FE model, necessary to obtain the load capacity consistent with the experimental...
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Organizational Wisdom: The Impact of Organizational Learning on the Absorptive Capacity of an Enterprise
PublicationPurpose: In this article, we analyze the concept of organizational wisdom, indicating its key elements and verifieng the relationships between them. Design/Methodology/Approach: The study was conducted at Vive Textile Recycling Sp. z o.o in Poland. Empirical data was collected from 138 managers using the PAPI technique. Structural equation modelling (SEM) was performed to test the research hypotheses. Additionally, the significance...
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Quantum strategies for rendezvous and domination tasks on graphs with mobile agents
PublicationThis paper explores the application of quantum nonlocality, a renowned and unique phenomenon acknowledged as a valuable resource. Focusing on an alternative application, we demonstrate its quantum advantage for mobile agents engaged in specific distributed tasks without communication. The research addresses the significant challenge of rendezvous on graphs and introduces a distributed task for mobile agents grounded in the graph...
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A collection of directed graphs for the minimum cycle mean weight computation
Open Research DataThis dataset contains definitions of the 16 directed graphs with weighted edges that were described in the following paper: Paweł Pilarczyk, A space-efficient algorithm for computing the minimum cycle mean in a directed graph, Journal of Mathematics and Computer Science, 20 (2020), no. 4, 349--355, DOI: 10.22436/jmcs.020.04.08, URL: http://dx.doi.org/10.22436/jmcs.020.04.08 These...