## Taiwanese Journal of Mathematics

### THE SHARP LOWER BOUND FOR THE SPECTRAL RADIUS OF CONNECTED GRAPHS WITH THE INDEPENDENCE NUMBER

#### Abstract

In this paper, we investigate some properties of the Perron vector of connected graphs. These results are used to characterize all extremal connected graphs which attain the minimum value among the spectral radii of all connected graphs with order $n=k\alpha$ and the independence number $\alpha$. Moreover, all extremal graphs which attain the maximum value among the spectral radii of clique trees with order $n=k\alpha$ and the independence number $\alpha$ are characterized.

#### Article information

Source
Taiwanese J. Math., Volume 19, Number 2 (2015), 419-431.

Dates
First available in Project Euclid: 4 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499133638

Digital Object Identifier
doi:10.11650/tjm.19.2015.4314

Mathematical Reviews number (MathSciNet)
MR3332305

Zentralblatt MATH identifier
1357.05083

#### Citation

Jin, Ya-Lei; Zhang, Xiao-Dong. THE SHARP LOWER BOUND FOR THE SPECTRAL RADIUS OF CONNECTED GRAPHS WITH THE INDEPENDENCE NUMBER. Taiwanese J. Math. 19 (2015), no. 2, 419--431. doi:10.11650/tjm.19.2015.4314. https://projecteuclid.org/euclid.twjm/1499133638

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