The Spectral Radii of Graphs with Prescribed Degree Sequence

- Journal title : Kyungpook mathematical journal
- Volume 54, Issue 3, 2014, pp.425-441
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2014.54.3.425

Title & Authors

The Spectral Radii of Graphs with Prescribed Degree Sequence

Li, Jianxi; Shiu, Wai Chee;

Li, Jianxi; Shiu, Wai Chee;

Abstract

In this paper, we first present the properties of the graph which maximize the spectral radius among all graphs with prescribed degree sequence. Using these results, we provide a somewhat simpler method to determine the unicyclic graph with maximum spectral radius among all unicyclic graphs with a given degree sequence. Moreover, we determine the bicyclic graph which has maximum spectral radius among all bicyclic graphs with a given degree sequence.

Keywords

pectral radius;degree sequence;unicyclic graph;bicyclic graph;

Language

English

References

1.

J. Bondy, U. Murty, Graph theory with applications, New York, MacMillan, 1976.

2.

T. Biyukoglu, J. Leydold,Graphs with given degree sequence and maximal spectral radius, Electron. J. Combin., 15(2008), #R119.

3.

F. Belardo, E. M. Li Marzi, S. K. Simic, J. Wang, On the spectral radius of unicyclic graphs with prescribed degree sequence, Linear Algebra. Appl., 432(2010), 2323-2334.

4.

D. Cvetkovic, M. Doob, H. Sachs, Spectra of Graphs: Theory and Applications, 3rd ed., Johan Ambrosius Barth Verlag, Heidelberg, Leipzig, 1995.

5.

D. Cvetkovic, P. Rowlinson, S. Simic, Eigenspaces of Graphs, Cambridge University Press, 1997.

6.

S. Guo, The spectral radius of unicyclic and bicyclic graphs with n vertices and k pendant vertices, Linear Algebra Appl., 408(2005), 78-85.

7.

X. He, Y. Liu, J. Shao, On the spectral radii of bicyclic graphs, J. Math. Res. Exposition., 27(2007), 445-454.

8.

A. Hoffman, J. Smith, On the spectral radii of topologically equivalent graphs, in: M. Fiedler (Ed.), Recent Advances in Graph Theory, Academia Praha, 1975, pp.273-281.

9.

R. Horn, C. Johnson, Matrix Analysis. Reprinted with corrections. Cambridge University Press, 1990.