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Search results for: STRONG PRODUCT GRAPHS
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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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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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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 the metric dimension of corona product graphs
PublicationWe give several results on the metric dimension of corona product graphs.
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On the super domination number of lexicographic product graphs
PublicationThe neighbourhood of a vertexvof a graphGis the setN(v) of all verticesadjacent tovinG. ForD⊆V(G) we defineD=V(G)\D. A setD⊆V(G) is called a super dominating set if for every vertexu∈D, there existsv∈Dsuch thatN(v)∩D={u}. The super domination number ofGis theminimum cardinality among all super dominating sets inG. In this article weobtain closed formulas and tight bounds for the super dominating number oflexicographic product...
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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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Bondage number of grid graphs
PublicationThe bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than the domination number of G. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some strong product and direct product of two paths.
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Product Graph Invariants with Applications in the Theory of Information
PublicationThere are a large number of graph invariants. In the paper, we consider some of them, e.g. the independence and chromatic numbers. It is well know that we cannot efficiently calculate these numbers for arbitrary graphs. In the paper we present relations between these invariants and concepts from the theory of information. Concepts such as source coding and transmission over a noisy channel with zero probability of error are modeled...
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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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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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The impact of end-user participation in IT projects on product usability
PublicationMany companies implementing new IT projects encounter numerous problems with ensuring good final product usability. The strong market competition they experience often results in necessity of undertaking difficult decisions with regard to cost minimization. This may force cuts in usability expertise and consulting, most often by limiting end-user participation in the project. However, it may also result in serious consequences...
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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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Relations between the domination parameters and the chromatic index of a graph
PublicationIn this paper we show bounds for the sum and the product of the domination parameters and the chromatic index of a graph. We alsopresent some families of graphs for which these bounds are achieved.
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Weakly convex and convex domination numbers of some products of graphs
PublicationIf $G=(V,E)$ is a simple connected graph and $a,b\in V$, then a shortest $(a-b)$ path is called a $(u-v)$-{\it geodesic}. A set $X\subseteq V$ is called {\it weakly convex} in $G$ if for every two vertices $a,b\in X$ exists $(a-b)$- geodesic whose all vertices belong to $X$. A set $X$ is {\it convex} in $G$ if for every $a,b\in X$ all vertices from every $(a-b)$-geodesic belong to $X$. The {\it weakly convex domination number}...
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How to meet when you forget: log-space rendezvous in arbitrary graphs
PublicationTwo identical (anonymous) mobile agents start from arbitrary nodes in an a priori unknown graph and move synchronously from node to node with the goal of meeting. This rendezvous problem has been thoroughly studied, both for anonymous and for labeled agents, along with another basic task, that of exploring graphs by mobile agents. The rendezvous problem is known to be not easier than graph exploration. A well-known recent result...
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Cobalt(II) and Cobalt(III) Tri‐tert‐butoxysilanethiolates. Synthesis, Properties, Crystal and Molecular Structures of [Co{μ‐SSi(OBut)3}{SSi(OBut)3}(NH3)]2 and [Co{SSi(OBut)3}2(NH3)4][SSi(OBut)3] Complexes
PublicationThe heteroleptic neutral tri‐tert‐butoxysilanethiolate of cobalt(II) incorporating ammonia as additional ligand (1) has been prepared by the reaction of a cobalt(II) ammine complex with tri‐tert‐butoxysilanethiol in water. Complex 1, dissolved in hexane, undergoes oxidation in an ammonia saturated atmosphere to the ionic cobalt(III) compound 2. Molecular and...
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The complexity of minimum-length path decompositions
PublicationWe consider a bi-criteria generalization of the pathwidth problem, where, for given integers k, l and a graph G, we ask whether there exists a path decomposition P of G such that the width of P is at most k and the number of bags in P, i.e., the length of P, is at most l. We provide a complete complexity classification of the problem in terms of k and l for general graphs. Contrary to the original pathwidth problem, which is fixed-parameter...
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A facile structural manipulation strategy to prepare ultra-strong, super-tough, and thermally stable polylactide/nucleating agent composites
PublicationPolylactide (PLA) is a biodegradable thermoplastic widely used in diferent felds, but it should be adequately modifed considering high-performance applications. However, the current processes for developing PLA materials achieve high strength at the expense of toughness or ductility of the materials. Therefore, there is need to develop new strategies for generation of PLA materials with high strength, great toughness, good ductility,...
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Pączkowanie - metoda rozwoju interoperacyjnych komponentów dla systemów rozproszonych = Budding – the software development method of interoperable components for distributed systems
PublicationPrzedstawiono 2 współczesne metody wytwarzania oprogramowania: iteracyjno-przyrostową oraz techniki zwinne, ich zalety i wady w kontekście budowy interoperacyjnych platform i środowisk rozproszonych. Zaprezentowano metodę rozwoju oprogramowania przez pączkowanie, jej założenia, zalety i wady. Przedstawiono technologie, na bazie których działa metodologia wytwarzania oprogramowania przez pączkowanie: Software Product Line, Enterprise...
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