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

Generalized inverse of the Laplacian matrix and some applicationsI. Gutman and W. XiaoFaculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia and MontenegroDepartment 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.
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