Taiwanese Journal of Mathematics

A (FORGOTTEN) UPPER BOUND FOR THE SPECTRAL RADIUS OF A GRAPH

Clive Elphick and Chia-An Liu

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Abstract

The best degree-based upper bound for the spectral radius is due to Liu and Weng. This paper begins by demonstrating that a (forgotten) upper bound for the spectral radius dating  from 1983 is equivalent to their much more recent bound. This bound is then used to compare lower bounds for the clique number. A series of line graph degree-based upper bounds for the Q-index is then proposedand compared experimentally with a graph based bound. Finally a new lower bound for generalised $r$-partite graphs is proved, by extending a result due to Erdős.

Article information

Source
Taiwanese J. Math., Volume 19, Number 6 (2015), 1593-1602.

Dates
First available in Project Euclid: 4 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499133728

Digital Object Identifier
doi:10.11650/tjm.19.2015.5393

Mathematical Reviews number (MathSciNet)
MR3434266

Zentralblatt MATH identifier
1357.05079

Subjects
Primary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.) 15A18: Eigenvalues, singular values, and eigenvectors

Keywords
graph spectral radius Q-index clique number

Citation

Elphick, Clive; Liu, Chia-An. A (FORGOTTEN) UPPER BOUND FOR THE SPECTRAL RADIUS OF A GRAPH. Taiwanese J. Math. 19 (2015), no. 6, 1593--1602. doi:10.11650/tjm.19.2015.5393. https://projecteuclid.org/euclid.twjm/1499133728


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