Algebraic connectivity for vertex-deleted subgraphs, and a notion of vertex centrality

Let G be a connected graph, suppose that v is a vertex of G, and denote the subgraph formed from G by deleting vertex v by G?v. Denote the algebraic connectivities of G and G?v by α(G) and α(G?v), respectively. In this paper, we consider the functions ?(v)=α(G)−α(G?v) and , provide attainable upper and lower bounds on both functions, and characterise the equality cases in those bounds. The function κ yields a measure of vertex centrality, and we apply that measure to analyse certain graphs arising from food webs.     

Spanning Euler tours and spanning Euler families in hypergraphs with particular vertex cuts

An Euler tour in a hypergraph is a closed walk that traverses each edge of the hypergraph exactly once, while an Euler family, first defined by Bahmanian and ?ajna, is a family of closed walks that jointly traverse each edge exactly once and cannot be concatenated. In this paper, we study the notions of a spanning Euler tour and a spanning Euler family, that is, an Euler tour (family) that also traverses each vertex of the hypergraph at least once. We examine necessary and sufficient conditions for a hypergraph to admit a spanning Euler family, most notably when the hypergraph possesses a vertex cut consisting of vertices of degree two. Moreover, we characterise hypergraphs with a vertex cut of cardinality at most two that admit a spanning Euler tour (family). This result enables us to reduce the problem of existence of a spanning Euler tour (which is NP-complete), as well as the problem of a spanning Euler family, to smaller hypergraphs.     

Generalized Calabi-Yau manifolds and the chiral de Rham complex

We show that the chiral de Rham complex of a generalized Calabi-Yau manifold carries N=2 supersymmetry. We discuss the corresponding topological twist for this N=2 algebra. We interpret this as an algebroid version of the super-Sugawara or Kac-Todorov construction.     

Study of a lacunary solid phase II—Morphological and kinetic characteristics of its formation

The morphological changes which take place during the formation of the lacunary phase αH₂C₂O₄·BaC₂O₄ by isothermal dehydration of the oxalate H₂C₂O₄·BaC₂O₄·2H₂O, are characteristic for dihydrations of hydrates which, with water vapor, form a divariant system.They show that the transformation affects the entire bulk of the solid from the very first moments of the reaction. The dihydrate crystal undergo a very regular fragmentation and the pseudomorph appears as a stacking of microcrystals whose shape and dimensions are unique and independent of the size and habit of the initial crystals.The kinetic characteristics of the reaction show that the microcrystal dimensions do not depend on dehydration rate, they enable the precise role of crystalline faces in gas evacuation to be evaluated.The origin of fragmentation, the microcrystal habit produced, the anisotropy of transformation of the crystalline faces and the process of water elimination are explained by means of structural considerations.     

AB initio SCF LCAO MO study of the HOH…Cl− hydrogen bond

Ab initio SCF LCAO MO calculations for the [H₂O…Cl]^? complex have been performed. The energy of the linear hydrogen bond has been found to be lower than the energy of the bifurcated one. The difference of the energies is about 3 kcal/mole. The calculated equilibrium distance between the oxygen and chlorine atoms equals 5.75 au. The interaction energy of the chlorine anion and the rigid water molecule amounts to ?19 kcal/mole. The optimization of the OH bond length in the complex (linear hydrogen bond) leads to an interaction energy of ?19.5 kcal/mole (the experimental value equals ?13.1 kcal/mole). As a result of the hydrogen bond formation the OH bond length increases by 0.08 au.     

Comparative superoxide dismutase activity studies

Our results indicate that the various methods for measurement of superoxide dismutase (SOD) activity differ considerably as regards sensitivity. The activity difference may be particularly striking in the determination of the SOD activities of crude homogenates, because of the large number of disturbing factors. We consider the epinephrine-adrenochrome method to be the most suitable for measurement of the SOD activities of crude homogenates and purified enzyme preparations.     

Reactions of hydroxyl radicals with polystyrene

The reaction of polystyrene with hydroxyl radicals, generated by the photolysis (λ > 300 nm) of H₂O₂, has been studied at 25° in dichloromethane solution, both under vacuum conditions and in presence of O₂. Spectroscopic analyses suggest the presence of phenols and hydroxymucondialdehydes (when O₂ is present) among the reaction products, indicating that OH addition occurs at the phenyl groups of the polymer. By comparison with initiated oxidation reactions under the same conditions, it is concluded that the OH radicals undergo mainly addition reactions. A mechanism has been produced to account for the products. The significance of OH addition reactions in the oxidation of polystyrene is considered, the OH radicals being produced by hydroperoxide decomposition during oxidation, and the products having been previously identified as containing mucondialdehydes.     

Coloring graphs by iterated local search traversing feasible and infeasible solutions

Graph coloring is one of the hardest combinatorial optimization problems for which a wide variety of algorithms has been proposed over the last 30 years. The problem is as follows: given a graph one has to assign a label to each vertex such that no monochromatic edge appears and the number of different labels used is minimized. In this paper we present a new heuristic for this problem which works with two different functionalities. One is defined by two greedy subroutines, the former being a greedy constructive one and the other a greedy modification one. The other functionality is a perturbation subroutine, which can produce also infeasible colorings, and the ability is then to retrieve feasible solutions. In our experimentation the proper tuning of this optimization scheme produced good results on known graph coloring benchmarks.     

A polyhedral study of the generalized vertex packing problem

The traditional vertex packing problem defined on an undirected graph identifies the largest weighted independent set of nodes, that is, a set of nodes whose induced subgraph contains no edges. In this paper, we examine a generalized vertex packing problem (GVP-k) in which k ``violations' to the independent set restriction are permitted, whereby k edges may exist within the subgraph induced by the chosen set of nodes. A particular context in which such problems arise is in the national airspace planning model of Sherali, Smith, and Trani (2000), where a set of flight-plans need to be composed for various flights subject to conflict, workload, and equity considerations. The GVP-k structure arises in modeling the air-traffic control sector workload restrictions, which stipulate that for each sector and during each discretized time-slot, the number of aircraft conflicts that would need to be resolved should not exceed k, for some k≥1. We derive several classes of facetial valid inequalities for GVP-k for certain specially structured subgraphs, identifying polynomial-sized convex hull representations for some of these cases. Related constraint generation routines are also developed, and some computational results are provided to demonstrate the efficacy of utilizing the proposed valid inequalities in solving GVP-k for different values of k.     

Inequalities for vertex distances of two simplices

We establish in this paper some inequalities for vertex distances of two simplices, and give some applications thereof.