Guaranteed lower bounds for eigenvalues

Some Lower Bounds for Estrada Index

Sharp Bounds on the PI Spectral Radius

In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.

A note on the bounds of Laplacian-energy-like-invariant

The Laplacian-energy-like of a simple connected graph G is defined as LEL:=LEL(G)=∑_(i=1)^n√(μ_i ), Where μ_1 (G)≥μ_2 (G)≥⋯≥μ_n (G)=0 are the Laplacian eigenvalues of the graph G. Some upper and lower bounds for LEL are presented in this note. Moreover, throughout this work, some results related to lower bound of spectral radius of graph are obtained using the term of ΔG as the num...

Guaranteed lower eigenvalue bounds for the biharmonic equation

The computation of lower eigenvalue bounds for the biharmonic operator in the buckling of plates is vital for the safety assessment in structural mechanics and highly on demand for the separation of eigenvalues for the plate’s vibrations. This paper shows that the eigenvalue provided by the nonconformingMorley finite element analysis, which is perhaps a lower eigenvalue bound for the biharmonic...

On the eigenvalues of some matrices based on vertex degree

The aim of this paper is to compute some bounds of forgotten index and then we present spectral properties of this index. In continuing, we define a new version of energy namely ISI energy corresponded to the ISI index and then we determine some bounds for it.