Spectral characterization of families of split graphs

An upper bound for the sum of the squares of the entries of the principal eigenvector corresponding to a vertex subset inducing a k-regular subgraph is introduced and applied to the determination of an upper bound on the order of such induced subgraphs. Furthermore, for some connected graphs we establish a lower bound for the sum of squares of the entries of the principal eigenvector corresponding to the vertices of an independent set. Moreover, a spectral characterization of families of split graphs, involving its index and the entries of the principal eigenvector corresponding to the vertices of the maximum independent set is given. In particular, the complete split graph case is highlighted

Relations between (κ, τ)-regular sets and star complements

Let G be a finite graph with an eigenvalue μ of multiplicity m. A set X of m vertices in G is called a star set for μ in G if μ is not an eigenvalue of the star complement G\X which is the subgraph of G induced by vertices not in X. A vertex subset of a graph is (k ,t)-regular if it induces a k -regular subgraph and every vertex not in the subset has t neighbors in it. We investigate the graphs having a (k,t)-regular set which induces a star complement for some eigenvalue. A survey of known results is provided and new properties for these graphs are deduced. Several particular graphs where these properties stand out are presented as examples

A proposed methodology for the correction of the Leaf Area Index measured with a ceptometer for pinus and eucalyptus forests = Proposta de uma methodologia para a correcao do indice de area foliar medido pelo ceptometro em provoamentos de pinus e eucalyptus

Leaf area index (LAI) is an important parameter controlling many biological and physiological processes associated with vegetation on the Earth's surface, such as photosynthesis, respiration, transpiration, carbon and nutrient cycle and rainfall interception. LAI can be measured indirectly by sunfleck ceptometers in an easy and non-destructive way but this practical methodology tends to underestimated when measured by these instruments. Trying to correct this underestimation, some previous studies heave proposed the multiplication of the observed LAI value by a constant correction factor. The assumption of this work is LAI obtained from the allometric equations are not so problematic and can be used as a reference LAI to develop a new methodology to correct the ceptometer one. This new methodology indicates that the bias (the difference between the ceptometer and the reference LAI) is estimated as a function of the basal area per unit ground area and that bias is summed to the measured value. This study has proved that while the measured Pinus LAI needs a correction, there is no need for that correction for the Eucalyptus LAI. However, even for this last specie the proposed methodology gives closer estimations to the real LAI values