On the Randić index and conditional parameters of a graph

Abstract

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 $n\times n$ matrix $\mathcal{A}$ whose ($i,j$)-entry is $$a_{ij}=\{\begin{array}{ll}\frac{1}{\sqrt{{\delta }_i{\delta }_j}}& \mathrm{if}{v}_i\sim v_j;\\ 0& \mathrm{otherwise},\end{array}$$ where ${\delta }_i$ denotes the degree of the vertex $v_i$. We study the Randić index and some interesting particular cases of conditional excess, conditional Wiener index, and conditional diameter. In particular, using the matrix $\mathcal{A}$ or its eigenvalues, we obtain tight bounds on the studied parameters.

arXiv admin note: text overlap with arXiv:math/0602437

References in corpus (1)

• The (a,b,s,t)-diameter of graphs: a particular case of conditional diameter

Cited by in corpus (2)

• Computational and analytical studies of the Randić index in Erdös-Rényi models
• Arithmetic-Geometric Spectral Radius of Trees and Unicyclic Graphs