Recent results on graphs with convex quadratic stability number

The main results about graphs with convex quadratic stability number (that is, graphs for which the stability number can be determined by convex quadratic programming) are surveyed including the most recently obtained. Furthermore, a few algorithmic techniques for the recognition of this type of graphs in particular families are presented

Reconhecimento de grafos com número de estabilidade quadrático convexo

São apresentados os principais e mais recentes resultados sobre grafos com número de estabilidade quadrático convexo (que são grafos cujo número de estabilidade pode ser determinado através de técnicas de programação quadrática convexa) e descritas algumas estratégias algorítmicas para o reconhecimento de grafos deste tipo em famílias particulares

Uncoupling the sensory effects of 1-Methylcyclopropene and Ripening stage on 'Hayward' Kiwifruit

'Hayward' kiwifruit were treated with 0.5 μL·L-1 of 1-methylcyclopropene (1- MCP) and stored in air at 0 °C. Treatment with 1-MCP reduced softening of kiwifruit during storage but did not affect soluble solids or titratable acidity. Sensory analyses were performed by a consumer panel and by trained panelists after 41, 77, and 161 days in storage. 1-MCP treatment negatively affected consumer preference, expressed as degree of liking. The trained panel clearly perceived 1-MCP-treated kiwifruit after 41 days in storage at 0 °C as more sour and firmer but less juicy, less sweet, and less flavorful than untreated fruit. After 161 days in storage, the perceived differences between 1-MCP-treated and untreated fruit had been reduced for sweetness and acidity, but the panel perceived 1-MCP-treated fruit as firmer and lagging behind in the ripening process. Altering the poststorage ripening rate, by placing 1-MCP-treated fruit at a higher temperature than untreated controls, allowed fruit to develop in such a way that a sensory panel was unable to distinguish between treatments. This result indicates that 1-MCP-treated fruit can be perceived by the consumer as similar to untreated fruit if adequately conditioned.info:eu-repo/semantics/publishedVersio

Algorithmic strategies for the recognition of graphs with convex

A major difficulty in the recognition of graphs with convex quadratic stability number is the existence of adverse subgraphs (an adverse subgraph is a subgraph such that the smallest eigenvalue of its adjacency matrix doesn’t change when any vertex or the neighbourhood of any vertex is deleted). It is a challenge to find adverse graphs without convex quadratic stability number. We present the main results about graphs with convex quadratic stability number and conclusions about the existence of adverse subgraphs belonging to this family in certain classes of graphs

Determination of (0,2)-regular sets in graphs

An eigenvalue of a graph is main iff its associated eigenspace is not orthogonal to the all-one vector j. The main characteristic polynomial of a graph G with p main distinct eigenvalues is _ (λ)=λ^−_0 λ^(−1)−_1 λ^(−2)-…-_(−2) λ−_(−1) and it has integer coefficients. If G has n vertices, the nxk walk matrix of G is _=(j,_j,_^"2" "j",…,_^(−) j) and W, the walk matrix of G, is _ for which rank(_)=k. The number k coincides with the number of distinct main eigenvalues of G. In [2] it was proved that the coefficients of the main characteristic polynomial of G are the solutions of =_^j. A (,)- regular set [3] is a subset of the vertices of a graph inducing a -regular subgraph such that every vertex not in the subset has neighbors in it. In [1], a strategy for the determination of (0,1)-regular sets is described and we generalize it in order to solve the problem of the determination of (0,2)-regular sets in arbitrary graphs. An algorithm for deciding whether or not a given graph has a (0,2)-regular set is described. Its complexity depends on the multiplicity of −2 as an eigenvalue of the adjacency matrix of the graph. When such multiplicity is low, the generalization of the results in [1] assure that the algorithm is polynomial. An example of application of the algorithm to a graph for which this multiplicity is low is also presented

How to solve the maximum matching problem determining (0,2)-regular sets

A (K-1)-regular set in a graph is a subset of vertices such that each vertex in the set hask neighbours in it and each vertex not in the set has exactly i neighbours in it.info:eu-repo/semantics/publishedVersio

Efficient domination through eigenvalues

The paper begins with a new characterization of (k, τ )-regular sets. Then, using this result as well as the theory of star complements, we derive a simplex-like algorithm for determining whether or not a graph contains a (0, τ )-regular set. When τ = 1, this algorithm can be applied to solve the efficient dominating set problem which is known to be NPcomplete. If −1 is not an eigenvalue of the adjacency matrix of the graph, this particular algorithm runs in polynomial time. However, although it doesn’t work in polynomial time in general, we report on its successful application to a vast set of randomly generated graphs

Avaliação da produção primária líquida em povoamentos puros e mistos de Quercus pyrenaica Willd. e Pinus pinaster L. no Distrito de Vila Real

Com este trabalho procurou-se quantificar a Produção Primária Líquida (PPL) de povoamentos puros e mistos de Pinus pinaster e de Quercus pyrenaica. A quantificação baseou-se em parcelas de amostragem do último Inventário Florestal Nacional (IFN) localizadas exclusivamente no Distrito de Vila Real. Deste trabalho resultou, pela primeira vez, a avaliação de valores de PPL, logo a possibilidade de quantificar a capacidade que estes ecossistemas têm em fixar carbono. Procedeu-se à comparação entre a performance dos povoamentos puros e mistos. Os resultados obtidos apontam para uma maior potencialidade produtiva dos povoamentos mistos, comparativamente aos povoamentos puros, ainda que não estatisticamente significativa

Antioxidant properties and fruit quality during long-term storage of “rocha” pear: effects of maturity and storage conditions

Free radical scavenging activity and the content of ascorbic acid and glutathione were investigated during long-term storage of the pear (Pyrus communis L. ‘Rocha’) fruit harvested at different maturity stages, stored in air or under controlled atmosphere and subjected to postharvest treatments with diphenylamine (DPA) and 1-methylcyclopropene (1-MCP). Harvest maturity had a significant effect on storage disorders, fruit firmness, soluble solids content and acidity. Differences in ascorbate content and free radical scavenging activity at harvest did not persist during storage. Controlled atmosphere and DPA strongly reduced the incidence and severity of browning disorders and superficial scald, whereas 1-MCP provided the most effective control. Neither DPA nor 1-MCP affected the free radical scavenging activityinfo:eu-repo/semantics/publishedVersio