Taiwanese Journal of Mathematics

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

Ya-Lei Jin and Xiao-Dong Zhang

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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

Subjects
Primary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.) 05C35: Extremal problems [See also 90C35]

Keywords
spectral radius independence number Perron vector clique tree

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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