An eigenvalue localization theorem for stochastic matrices and its application to Randić matrices

Abstract

A square matrix is called stochastic (or row-stochastic) if it is non-negative and has each row sum equal to unity. Here, we constitute an eigenvalue localization theorem for a stochastic matrix, by using its principal submatrices. As an application, we provide a suitable bound for the eigenvalues, other than unity, of the Randić matrix of a connected graph.

On <em>ev</em>-degree and <em>ve</em>-degree topological indices

“…We refer the interested reader to [8][9][10] and the references therein for the up to date arguments about the Randić index.…”

Predicting Some Physicochemical Properties of Octane Isomers: A Topological Approach Using <em>ev</em>-Degree and <em>ve</em>-Degree Zagreb Indices<strong> </strong>

“…We refer the interested reader to [15][16][17] and the references therein for the up to date arguments about the Randić index. And now we give the definitions of ev-degree and ve-degree concepts which were given by Chellali et al…”

Predicting Some Physicochemical Properties of Octane Isomers: A Topological Approach Using &lt;i&gt;ev&lt;/i&gt;-Degree and &lt;i&gt;ve&lt;/i&gt;-Degree Zagreb Indices

“…The interested reader should see to [15][16][17] and the references therein for the up to date arguments about the Randić index. And now the definitions of ev-degree and ve-degree concepts are given which were given by Chellali et al in [5].…”