Subsets Of Same Size Research Articles

Isoperimetric Inequalities and Eigenvalues

An upper bound is given on the minimum distance between i subsets of same size of a regular graph in terms of the ith largest eigenvalue in absolute value. This yields a bound on the diameter in terms of the ith largest eigenvalue for any integer i. Our bounds are shown to be asymptotically tight for explicit families of graphs having an asymptotically optimal ith largest eigenvalue. A result by Quenell [Adv. Math., 106 (1994), pp. 122--148] relating the diameter, the second eigenvalue, and the girth of a regular graph is obtained as a by-product.

Some prediction procedures with special reference to selection

We consider the problem of prediction of an unobserved variable for a certain subset of a population in which mean or some other well defined function of criterion variable(s) is higher than that of any other subset of same size. To select this particular subpopulation, optimum decision rules - to be termed as selection indices, are constructed. We derived selection indices when selection is made in two or more stages. Optimum decision rules are obtained when there are constraints requiring that, in the selected part of the population, average values of some other criterion variables are above certain prespecified levels. More emphasis is given to two stage selection.