The aim of this paper is to study some parameters of simple graphs related
with the degree of the vertices. So, our main tool is the n×n matrix
A whose (i,j)-entry is aij={δiδj10ifvi∼vj;otherwise, where δi denotes the degree of the vertex vi. We study
the Randi\'{c} index and some interesting particular cases of conditional
excess, conditional Wiener index, and conditional diameter. In particular,
using the matrix A or its eigenvalues, we obtain tight bounds on the
studied parameters.Comment: arXiv admin note: text overlap with arXiv:math/060243