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Compatibility of Crude Oil Blends─Processing Issues Related to Asphaltene Precipitation, Methods of Instability Prediction─A Review
PublicationProcessing crude oil of variable composition, especially due to the need to process crude oil blends obtained from various sources, presents a tremendous process challenge. This is mainly due to the destabilization of the colloidal system manifested mostly by the precipitation of the asphaltene fraction. The precipitation of asphaltenes from crude oil is a serious problem during extraction, transport, and processing. In the latter...
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Quantification of Compatibility Between Polymeric Excipients and Atenolol Using Principal Component Analysis and Hierarchical Cluster Analysis
PublicationAn important challenge to overcome in the solid dosage forms technology is the selection of the most biopharmaceutically efficient polymeric excipients. The excipients can be selected, among others, by compatibility studies since incompatibilities between ingredients of the drug formulations adversely affect their bioavailability, stability, efficacy, and safety. Therefore, new, fast, and reliable methods for detecting incompatibility...
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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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Interval incidence coloring of bipartite graphs
PublicationIn 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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The Backbone Coloring Problem for Small Graphs
PublicationIn this paper we investigate the values of the backbone chromatic number, derived from a mathematical model for the problem of minimization of bandwidth in radio networks, for small connected graphs and connected backbones (up to 7 vertices). We study the relationship of this parameter with the structure of the graph and compare the results with the solutions obtained using the classical graph coloring algorithms (LF, IS), modified...
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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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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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Colorings of the Strong Product of Circulant Graphs
PublicationGraph 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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Consecutive colorings of the edges of general graphs
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Weakly connected domination critical graphs
PublicationPraca dotyczy niektórych klas grafów krytycznych ze względu na liczbę dominowania słabo spójnego.
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Compact cyclic edge-colorings of graphs
PublicationArtykuł jest poświęcony modelowi zwartego cyklicznego kolorowania krawędzi grafów. Ten wariant kolorowania jest stosowany w modelowaniu uszeregowań w systemach produkcyjnych, w których proces produkcyjny ma charakter cykliczny. W pracy podano konstrukcje grafów, które nie zezwalają na istnienie pokolorowania w rozważanym modelu. Wykazano także kilka własności teoretycznych, takich jak ograniczenia górne na liczbę kolorów w optymalnym...
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Paired domination and doubly domination in graphs
PublicationW rozprawie poruszane są zagadnienia związane z dominowaniem parami w grafach oraz domiowaniem totalno - powściągniętym w grafach. Ponadto omawiane są zagadnienia związane ze złożonością obliczeniową różnych problemów dominowania w grafach.
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Distance paired domination numbers of graphs
PublicationW pracy przedstawione są pewne własności liczb k-dominowania parami w grafach. Wykazane jest, że problem decyzyjny liczby k-dominowania parami jest problemem NP-zupełnym nawet dla grafów dwudzielnych. Przedstawione są ograniczenia górne i dolne dla liczby k-dominowania parami w drzewach i scharakteryzowane drzewa, w których te ograniczenia są osiągnięte.
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The complexity of equitable vertex coloring graphs
PublicationW artykule podajemy wzory na sprawiedliwą liczbę chromatyczną niektórych produktów grafowych. Ponadto przedstawiamy dwa algorytmy wielomianowe dla sprawiedliwego kolorowania grafów suboptymalną liczba kolorów.
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Equitable coloring of corona multiproducts of graphs
PublicationWe give some results regarding the equitable chromatic number for l-corona product of two graphs: G and H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G.
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Computational aspects of greedy partitioning of graphs
PublicationIn 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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On proper (1,2)‐dominating sets in graphs
PublicationIn 2008, Hedetniemi et al. introduced the concept of (1,)-domination and obtained some interesting results for (1,2) -domination. Obviously every (1,1) -dominating set of a graph (known as 2-dominating set) is (1,2) -dominating; to distinguish these concepts, we define a proper (1,2) -dominating set of a graph as follows: a subset is a proper (1,2) -dominating set of a graph if is (1,2) -dominating and it is not a (1,1) -dominating...
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Weakly connected Roman domination in graphs
PublicationA Roman dominating function on a graph G=(V,E) is defined to be a function f :V → {0,1,2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v)=2. A dominating set D⊆V is a weakly connected dominating set of G if the graph (V,E∩(D×V)) is connected. We define a weakly connected Roman dominating function on a graph G to be a Roman dominating function such that the set...
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2-outer-independent domination in graphs
PublicationWe 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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Distributed Evacuation in Graphs with Multiple Exits
PublicationWe consider the problem of efficient evacuation using multiple exits. We formulate this problem as a discrete problem on graphs where mobile agents located in distinct nodes of a given graph must quickly reach one of multiple possible exit nodes, while avoiding congestion and bottlenecks. Each node of the graph has the capacity of holding at most one agent at each time step. Thus, the agents must choose their movements strategy...
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On Computational Aspects of Greedy Partitioning of Graphs
PublicationIn this paper we consider a problem of graph P-coloring consisting in partitioning the vertex set of a graph such that each of the resulting sets induces a graph in a given additive, hereditary class of graphs P. We focus on partitions generated by the greedy algorithm. In particular, we show that given a graph G and an integer k deciding if the greedy algorithm outputs a P-coloring with a least k colors is NP-complete for an infinite...
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On the hardness of computing span of subcubic graphs
PublicationIn the paper we study the problem of finding ξ-colorings with minimal span, i.e. the difference between the largest and the smallest color used.
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Interval incidence coloring of subcubic graphs
PublicationIn this paper we study the problem of interval incidence coloring of subcubic graphs. In [14] the authors proved that the interval incidence 4-coloring problem is polynomially solvable and the interval incidence 5-coloring problem is N P-complete, and they asked if χii(G) ≤ 2∆(G) holds for an arbitrary graph G. In this paper, we prove that an interval incidence 6-coloring always exists for any subcubic graph G with ∆(G) = 3.
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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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Dynamic F-free Coloring of Graphs
PublicationA 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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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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The hat problem on a union of disjoint graphs
PublicationThe 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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Non-isolating 2-bondage in graphs
PublicationA 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 non-isolating 2-bondage number of G, denoted by b_2'(G), is the minimum cardinality among all sets of edges E' subseteq E such that delta(G-E') >= 1 and gamma_2(G-E') > gamma_2(G)....
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On the metric dimension of corona product graphs
PublicationWe give several results on the metric dimension of corona product graphs.
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A graph coloring approach to scheduling of multiprocessor tasks on dedicated machines with availability constraints
PublicationWe address a generalization of the classical 1- and 2-processor unit execution time scheduling problem on dedicated machines. In our chromatic model of scheduling machines have non-simultaneous availability times and tasks have arbitrary release times and due dates. Also, the versatility of our approach makes it possible to generalize all known classical criteria of optimality. Under these stipulations we show that the problem...
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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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Application of Graph Theory Algorithms in Non-disjoint Functional Decomposition of Specific Boolean Functions
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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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Bipartite theory of graphs: outer-independent domination
PublicationLet $G = (V,E)$ be a bipartite graph with partite sets $X$ and $Y$. Two vertices of $X$ are $X$-adjacent if they have a common neighbor in $Y$, and they are $X$-independent otherwise. A subset $D \subseteq X$ is an $X$-outer-independent dominating set of $G$ if every vertex of $X \setminus D$ has an $X$-neighbor in $D$, and all vertices of $X \setminus D$ are pairwise $X$-independent. The $X$-outer-independent domination number...
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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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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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Sum Coloring of Bipartite Graphs with Bounded Degree
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Graphs with convex domination number close to their order
PublicationW pracy opisane są grafy z liczbą dominowania wypukłego bliską ilości ich wierzchołków.
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Self-stabilizing algorithm for edge-coloring of graphs
PublicationReferat ten poświęcony jest kolorowaniu grafów w modelu rozproszonym.Podano samostabilizujący się algorytm kolorowania krawędzi grafu wraz z dowodem poprawności oraz oszacowaniem jego czasu działania.
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program verification strategy and edge ranking of graphs
PublicationW artykule rozważamy model, w którym zakładamy, że dany jest zbiór asercji/testów dla pewnych bloków programu. Celem jest znalezienie optymalnej, tzn. wymagającej wykonania minimalnej liczby testów strategii wyszukiwania błędu w kodzie programu. Pomimo założenia w modelu, iż program posiada dokładnie jeden błąd, rozważania można uogólnić na testowanie kodu z dowolną liczbą błędów. Analizujemy teoretyczne własności tego modelu oraz...
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Parallel query processing and edge ranking of graphs
PublicationArtykuł poświęcony jest problemowi szukania drzewa spinającego o minimalnym uporządkowanym indeksie chromatycznym. Jednym z zastosowań jest poszukiwanie optymalnych harmonogramów w równoległym przetwarzaniu zapytań w relacyjnych bazach danych. Podajemy nowe oszacowanie funkcji dobroci przybliżonego algorytmu autorstwa Makino, Uno i Ibaraki wraz z rezultatami testów komputerowych przeprowadzonych dla grafów losowych.
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Strong weakly connected domination subdivisible graphs
PublicationArtykuł dotyczy wpływu podziału krawędzi na liczbę dominowania słabo spójnego. Charakteryzujemy grafy dla których podział dowolnej krawędzi zmienia liczbę dominowania słabo spójnego oraz grafy dla których podział dowolnych dwóch krawędzi powoduje zmianę liczby dominowania słabo spójnego.
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On extremal sizes of locally k-tree graphs
PublicationA graph G is a locally k-tree graph if for any vertex v the subgraph induced by the neighbours of v is a k-tree, k>=0, where 0-tree is an edgeless graph, 1-tree is a tree. We characterize the minimum-size locally k-trees with n vertices. The minimum-size connected locally k-trees are simply (k + 1)-trees. For k >= 1, we construct locally k-trees which are maximal with respect to the spanning subgraph relation. Consequently, the...
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Edge and Pair Queries-Random Graphs and Complexity
PublicationWe 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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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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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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Graphs with equal domination and certified domination numbers
PublicationA setDof vertices of a graphG= (VG,EG) is a dominating set ofGif every vertexinVG−Dis adjacent to at least one vertex inD. The domination number (upper dominationnumber, respectively) ofG, denoted byγ(G) (Γ(G), respectively), is the cardinality ofa smallest (largest minimal, respectively) dominating set ofG. A subsetD⊆VGis calleda certified dominating set ofGifDis a dominating set ofGand every vertex inDhas eitherzero...
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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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Graphs hard-to-process for greedy algorithm MIN
PublicationWe compare results of selected algorithms that approximate the independence number in terms of the quality of constructed solutions. Furthermore, we establish smallest hard- to-process graphs for the greedy algorithm MIN.
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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.