The cut-set $$\partial (S)$$ of a graph $$G=(V,E)$$ is the set edges that have one endpoint in $$S\subset V$$ and other $$V\setminus S$$ , whenever G[S] connected, cut $$[S,V\setminus S]$$ G called connected cut. A bond an inclusion-wise minimal disconnecting G, i.e., bonds are cut-sets determine cuts such $$G[V\setminus both connected. Contrasting with large number studies related to maximum c...

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Investigation of reliability characteristics under fuzzy environments is proposed in this paper. Fuzzy Weibull distribution and lifetimes of components are using it described. Formulas of a fuzzy reliability function, fuzzy hazard function and their α-cut set are presented. Furthermore, the fuzzy functions of series systems and parallel systems are discussed, respectively. Finally, some num...

This paper defines and studies a new, interesting, and challenging benchmark problem that originates in systems biology. The minimal seed-set problem is defined as follows: given a description of the metabolic reactions of an organism, characterize the minimal set of nutrients with which it could synthesize all nutrients it is capable of synthesizing. Current methods used in systems biology yie...

We present the first polynomial-time algorithm for computing the minimal covering set of a (weak) tournament. The algorithm is based on a linear programming formulation of a subset of the minimal covering set known as the essential set. On the other hand, we show that no efficient algorithm exists for two variants of the minimal covering set, the minimal upward covering set and the minimal down...

CiteSeer is a freely available, online citation database. In this paper, we explore the citation graph of CiteSeer. First, we characterize that graph as given by CiteSeer. Second, considering a set of anchor papers, we give heuristics to find a partition of the graph whose cut is minimal. Finally, we evaluate our solution using different metrics.

This paper provides an analysis of capacitated network design cut–set polyhedra. We give a complete linear description of the cut–set polyhedron of the single commodity – single facility capacitated network design problem. Then we extend the analysis to single commodity – multifacility and multicommodity – multifacility capacitated network design problems. Valid inequalities described here are ...

In this article, we provide an overview on how the maximum weighted stable set problem can be solved exactly with Branch & Cut techniques. In addition, we provide selected references to other exact methods. We start with a brief introduction of the stable set problem and a few basic definitions but assuming that the reader is already familiar with the basic concepts. The main stress of this art...

We show how to express intuitionistic Zermelo set theory in deduction modulo (i.e. by replacing its axioms by rewrite rules) in such a way that the corresponding notion of proof enjoys the normalization property. To do so, we first rephrase set theory as a theory of pointed graphs (following a paradigm due to P. Aczel) by interpreting set-theoretic equality as bisimilarity, and show that in thi...

an equitable domination has interesting application in the contextof social networks. in a network, nodes with nearly equal capacitymay interact with each other in a better way. in the societypersons with nearly equal status, tend to be friendly. in thispaper, we introduce new variant of equitable domination of agraph. basic properties and some interesting results have beenobtained.