Bounds for Eigenvalues of a Graph

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.

Some Lower Bounds for Estrada Index

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...

Laplacian Sum-Eccentricity Energy of a Graph

We introduce the Laplacian sum-eccentricity matrix LS_e} of a graph G, and its Laplacian sum-eccentricity energy LS_eE=sum_{i=1}^n |eta_i|, where eta_i=zeta_i-frac{2m}{n} and where zeta_1,zeta_2,ldots,zeta_n are the eigenvalues of LS_e}. Upper bounds for LS_eE are obtained. A graph is said to be twinenergetic if sum_{i=1}^n |eta_i|=sum_{i=1}^n |zeta_i|. Conditions ...

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.

On net-Laplacian Energy of Signed Graphs

A signed graph is a graph where the edges are assigned either positive ornegative signs. Net degree of a signed graph is the dierence between the number ofpositive and negative edges incident with a vertex. It is said to be net-regular if all itsvertices have the same net-degree. Laplacian energy of a signed graph is defined asε(L(Σ)) =|γ_1-(2m)/n|+...+|γ_n-(2m)/n| where γ_1,...,γ_n are the ei...