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The aim of this paper is to study some parameters of simple graphs relatedwith the degree of the vertices. So, our main tool is the $n\times n$ matrix${\cal A}$ whose ($i,j$)-entry is $$ a_{ij}= \left\lbrace \begin{array}{ll}  \frac{1}{\sqrt{\delta_i\delta_j}} & {\rm if }\quad v_i\sim v_j ;  \\ 0 & {\rm otherwise,} \end{array}  \right. $$ where $\delta_i$ denotes the degree of the vertex $v_i$. We studythe Randi\'{c} index and some interesting particular cases of conditionalexcess, conditional Wiener index, and conditional diameter. In particular,using the matrix ${\cal A}$ or its eigenvalues, we obtain tight bounds on thestudied parameters.

On the Randi\'{c} index and conditional parameters of a graph