EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXIX, No. 29, pp. 15–23 (2004)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home


Pick a mirror


Generalized inverse of the Laplacian matrix and some applications

I. Gutman and W. Xiao

Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia and Montenegro
Department of Computer Science, South China University of Technology, Guangzhou 510641, P. R. China, and Xiamen University, P. O. Box 1003, Xiamen 361005, P. R. China

Abstract: The generalized inverse $L^\dagger$ of the Laplacian matrix of a connected graph is examined and some of its properties are established. In some physical and chemical considerations the quantity $r_{ij} = (L^\dagger)_{ii} + (L^\dagger)_{jj} - (L^\dagger)_{ij} - (L^\dagger)_{ji}$ is encountered; it is called resistance distance. Based on the results obtained for $L^\dagger$ we prove some previously known and deduce some new properties of the resistance distance.

Keywords: Laplacian matrix; Laplacian eigenvector (of a graph); Laplacian eigenvalue (of a graph); resistance distance

Classification (MSC2000): 05C50

Full text of the article: (for faster download, first choose a mirror)

Electronic fulltext finalized on: 6 Oct 2003. This page was last modified: 20 Jun 2011.

© 2003 Mathematical Institute of the Serbian Academy of Science and Arts
© 2003–2011 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition