Some sharp lower bounds for spectral radius of connected graphs

GONG He-lin

Issue 4

Dec. 2014

Turn off MathJax

Article Contents

Article Navigation > Journal of East China Normal University (Natural Sciences) > 2012 > (4): 18-26

GONG He-lin. Some sharp lower bounds for spectral radius of connected graphs[J]. Journal of East China Normal University (Natural Sciences), 2012, (4): 18-26.

Citation:

GONG He-lin. Some sharp lower bounds for spectral radius of connected graphs[J]. Journal of East China Normal University (Natural Sciences), 2012, (4): 18-26.

GONG He-lin. Some sharp lower bounds for spectral radius of connected graphs[J]. Journal of East China Normal University (Natural Sciences), 2012, (4): 18-26.

Citation:

GONG He-lin. Some sharp lower bounds for spectral radius of connected graphs[J]. Journal of East China Normal University (Natural Sciences), 2012, (4): 18-26.

PDF( 201 KB)

Some sharp lower bounds for spectral radius of connected graphs

GONG He-lin

1.
School of Mathematics and Computer Science, Shangrao Normal University, Shangrao Jiangxi 334001, China

Received Date: 2011-08-01
Rev Recd Date: 2011-11-01
Publish Date: 2012-07-25

Abstract

Abstract

This paper studied lower bounds on the spectral radius of connected simple graphs and proved an useful inequality for the number of walks. Furthermore, some new lower bounds on the spectral radius of graphs were provided in terms of the maximum and minimum degree, the average degree, the 2-degree and the number of $k$-walks(with $k$ vertexes). By applying the properties of similar matrices and the Weyl inequalities, another lower bound was obtained by means of the number of $k$-walks. Simultaneously, all extremal graphs which achieve above bounds were also characterized.
- adjacency matrix,
- spectral radius,
- Perron eigenvector,
- lower bound

FullText(HTML)

References(1)

References

[1]

{1} YU A M, LU M, TIAN F. On the spectral radius of graphs[J]. Linear Algebra Appl, 2004, 387: 41-49.
{2} NIKIFOROV V. Walks and the spectral radius of graphs[J]. Linear Algebra Appl, 2006, 418: 257-268.
{3} HORN R A, JOHNSON C R. Matrix Analysis[M]. Cambridge: Cambridge University Press, 1985.
{4} CVETKOVJ\'{C} D, DOOB M, SACHS H. Spectra of Graphs-Theory and Application[M]. New York: Academic Press, 1980.
{5} HONG Y. Bounds of eigenvalues of graphs[J]. Discrete Math, 1993, 123: 65-74.
{6} DAS K, KUMAR P. Some new bounds on the spectral radius of graphs[J]. Discrete Math, 2004, 281: 149-161.
{7} HOFMEISTER M. Spectral radius and degree sequence[J]. Math Nachr, 1988, 139: 37-44.
{8} HONG Y, ZHANG X D. Sharp upper and lower bounds for the Laplacian matrices of trees[J]. Discrete Math, 2005, 296: 187-197.
{9} HU S B. A sharp lower bound of the spectral radius of simple graphs[J]. Anal Discrete Math, 2009, 3: 379-385.
{10} SHI L S. Bounds on the (Laplacian) spectral radius of graphs[J]. Linear Algebra Appl, 2007, 422: 755-770.
{11} YU A M. A new upper bound for the laplacian spectral radius of a graph[J]. Electronic Journal of Linear Algebra, 2010, 20: 730-738.

Relative Articles

Supplements(0)

Cited By

Proportional views