Covering Energy of Some Classes of Posets

Abstract

The concept of the covering energy of a poset is introduced and its bounds are given. We compute covering energy of some classes of posets like S<sub>n</sub>, 2<sup>n</sup>. The posets D<sub>k</sub> and D<sup>'</sup><sub>k</sub> are defined and two recurrence relations for the characteristic polynomials of these posets are obtained. The energies of the posets D<sub>1</sub>, D<sub>2</sub>, D<sub>3</sub>, D<sub>4</sub> and D<sub>5</sub> are explicitly computed. The existence of some eigenvalues for some type of D<sub>k</sub> and D<sup>'</sup><sub>k</sub> is proved.