Advanced search
Publication Cover
Linear and Multilinear Algebra Volume 59, 2011 - Issue 3
Submit an article Journal homepage
167
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

An edge-grafting theorem on Laplacian spectra of graphs and its application

Mingqing Zhai Department of Mathematics, East China Normal University, Shanghai, 200241, China; Department of Mathematics, Chuzhou University, Anhui, Chuzhou, 239012, China
,
Ruifang Liu Department of Mathematics, East China Normal University, Shanghai, 200241, China
&
Jinlong Shu Department of Mathematics, East China Normal University, Shanghai, 200241, China; Key Laboratory of Geographic Information Science, Ministry of Education East China Normal University, Shanghai, 200241, ChinaCorrespondence[email protected]
Pages 303-315 | Received 25 Oct 2008, Accepted 13 Oct 2009, Published online: 25 Feb 2011

References

  • Anderson , WN and Morley , TD . 1985 . Eigenvalues of the Laplacian of a graph . Linear Multilinear Algebra , 18 : 141 – 145 .
  • Brualdi , RA and Solheid , ES . 1986 . On the spectral radius of complementary acyclic matrices of zeros and ones . SIAM J. Algebra Discrete Method , 7 : 265 – 272 .
  • Grone , R , Merris , R and Sunder , VS . 1990 . The Laplacian spectrum of a graph : II . SIAM J. Matrix Anal. Appl. , 11 : 218 – 238 .
  • Guo , JM . 2006 . The effect on the Laplacian spectral radius of a graph by adding or grafting edges . Linear Algebra Appl. , 413 : 59 – 71 .
  • Guo , JM . 2007 . The Laplacian spectral radius of a graph under perturbation . Comput. Math. Appl. , 54 : 709 – 720 .
  • Guo , SG . 2001 . The largest eigenvalues of Laplacian matrix of unicyclic graphs . Appl. Math. J. Chinese Univ. Ser. A. , 16 : 131 – 135 .
  • Hong , Y and Zhang , XD . 2005 . Sharp upper and lower bounds for the largest eigenvalue of the Laplacian matrices of trees . Discrete Math. , 296 : 187 – 197 .
  • Li , JS and Zhang , XD . 1998 . On Laplacian eigenvalues of a graph . Linear Algebra Appl. , 285 : 305 – 307 .
  • Li , Q and Feng , K . 1979 . On the largest eigenvalues of graphs . Acta Math. Appl. Sin. , 2 : 167 – 175 . (in Chinese)
  • Liu , Y , Shao , JY and Yuan , XY . 2008 . Some results on the ordering of the Laplacian spectral radii of unicyclic graphs . Discrete Appl. Math. , 156 : 2679 – 2697 .
  • Merris , R . 1994 . Laplacian matrices of graphs: A survey . Linear Algebra Appl. , 197–198 : 143 – 176 .
  • Merris , R . 1998 . A note on the Laplacian graph eigenvalues . Linear Algebra Appl. , 285 : 33 – 35 .
  • Pan , YL . 2002 . Sharp upper bounds for the Laplacian graph eigenvalues . Linear Algebra Appl. , 355 : 287 – 295 .
  • Shu , JL , Hong , Y and Wenren , K . 2002 . A sharp upper bound on the largest eigenvalue of the Laplacian matrix of a graph . Linear Algebra Appl. , 347 : 123 – 129 .
  • Wu , BF , Xiao , EL and Hong , Y . 2005 . The spectral radius of trees on k pendant vertices . Linear Algebra Appl. , 395 : 343 – 349 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.