Tighter spectral bounds for the cut size, based on Laplacian eigenvectors

Tighter Cut-based Bounds for k-pairs Communication Problems

We study the extent to which combinatorial cut conditions determine the maximum network coding rate of k-pairs communication problems. We seek a combinatorial parameter of directed networks which constitutes a valid upper bound on the network coding rate but exceeds this rate by only a small factor in the worst case. (This worst-case ratio is called the gap of the parameter.) We begin by consid...

Spectral bounds for the maximum cut problem

The maximum cut problem this paper deals with can be formulated as follows. Given an undirected simple graph G = (V,E) where V and E stand for the node and edge sets respectively, and given weights assigned to the edges: (wij)ij∈E , a cut δ(S), with S ⊆ V is de ned as the set of edges in E with exactly one endnode in S, i.e. δ(S) = {ij ∈ E | |S ∩ {i, j}| = 1}. The weight w(S) of the cut δ(S) is...

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...

Bounds for the Laplacian spectral radius of graphs