Advanced search
Publication Cover
Linear and Multilinear Algebra Volume 63, 2015 - Issue 3
Submit an article Journal homepage
1,583
Views
42
CrossRef citations to date
0
Altmetric
Articles

Some results on resistance distances and resistance matrices

Lizhu SunSchool of Science, Harbin Institute of Technology, Harbin, P.R. China.
,
Wenzhe WangCollege of Science, Harbin Engineering University, Harbin, P.R. China.
,
Jiang ZhouCollege of Science, Harbin Engineering University, Harbin, P.R. China.;College of Computer Science and Technology, Harbin Engineering University, Harbin, P.R. China.Correspondence[email protected]
&
Changjiang BuCollege of Science, Harbin Engineering University, Harbin, P.R. China.Correspondence[email protected]
Pages 523-533 | Received 23 Sep 2013, Accepted 11 Dec 2013, Published online: 11 Jun 2014

References

  • Klein DJ, Randić M. Resistance distance. J. Math. Chem. 1993;12:81–95.
  • Bapat RB, Gupta S. Resistance distance in wheels and fans. Indian J. Pure Appl. Math. 2010;41:1–13.
  • Chen HY, Zhang FJ. Resistance distance and the normalized Laplacian spectrum. Discrete Appl. Math. 2007;155:654–661.
  • Gao X, Luo Y, Liu W. Kirchhoff index in line, subdivision and total graphs of a regular graph. Discrete Appl. Math. 2012;160:560–565.
  • Klein DJ. Resistance-distance sum rules. Croat. Chem. Acta. 2002;75:633–649.
  • Xiao WJ, Gutman I. Resistance distance and Laplacian spectrum. Theor. Chem. Acc. 2003;110:284–289.
  • Yang YJ, Klein DJ. A recursion formula for resistance distances and its applications. Discrete Appl. Math. 2013;161:2702–2715.
  • Zhang HP, Yang YJ, Li CW. Kirchhoff index of composite graphs. Discrete Appl. Math. 2009;157:2918–2927.
  • Zhou B, Trinajstić N. On resistance-distance and Kirchhoff index. J. Math. Chem. 2009;46:283–289.
  • Ben-Israel A, Greville TNE. Generalized inverses: theory and applications. 2nd ed. New York (NY): Springer; 2003.
  • Bapat RB. Graphs and matrices. London, New Delhi: Universitext, Springer, Hindustan Book Agency; 2010.
  • Bu C, Sun L, Zhou J, Wei Y. A note on block representations of the group inverse of Laplacian matrices. Electron. J. Linear Algebra. 2012;23:866–876.
  • Zhou J, Bu C, Wei Y. Group inverse for block matrices and some related sign analysis. Linear Multilinear Algebra. 2012;60:669–681.
  • Kirkland S, Neumann M, Shader B. Distances in weighted trees and group inverse of Laplacian matrices. SIAM J. Matrix Anal. Appl. 1997;18:827–841.
  • Zhou J, Sun L, Wang W, Bu C. Line star sets for Laplacian eigenvalues. Linear Algebra Appl. 2014;440:164–176.
  • Fallat S, Fan YZ. Bipartiteness and the least eigenvalue of signless Laplacian of graphs. Linear Algebra Appl. 2012;436:3254–3267.
  • Xiao WJ, Gutman I. Relations between resistance and Laplacian matrices and their applications. MATCH Commun. Math. Comput. Chem. 2004;51:119–127.
  • van Dam ER, Haemers WH. Which graphs are determined by their spectrum? Linear Algebra Appl. 2003;373:241–272.
  • Merris R. The distance spectrum of a tree. J. Graph Theory. 1990;14:365–369.

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.