The Minimum Spectral Radius of Graphs with the Independence Number

TL;DR

This paper characterizes extremal connected graphs with the minimum spectral radius among graphs with a fixed order and independence number, using properties of the Perron vector.

Contribution

It provides a new characterization of extremal graphs with minimum spectral radius based on Perron vector properties for graphs with given order and independence number.

Findings

Identifies extremal graphs with minimum spectral radius for given parameters

Uses Perron vector properties to characterize these graphs

Results applicable to spectral graph theory and graph optimization

Abstract

In this paper, we investigate some properties of the Perron vector of connected graphs. These results are used to characterize that all extremal connected graphs with having the minimum (maximum) spectra radius among all connected graphs of order $n=k\alpha$ with the independence number $\alpha$, respectively.