Geodesic
Generalized inverse of the Laplacian matrix and some applications
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 29 (2004), p. 15 .

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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.
DOI : 10.2298/BMAT0429015G
Classification : 05C50
Keywords: Laplacian matrix, Laplacian eigenvector (of graph), Laplacian eigenvalue (of graph), resistance distance 
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     title = {Generalized inverse of the {Laplacian} matrix and some applications},
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I. Gutman; W. Xiao. Generalized inverse of the Laplacian matrix and some applications. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 29 (2004), p. 15 . doi : 10.2298/BMAT0429015G. http://geodesic.mathdoc.fr/articles/10.2298/BMAT0429015G/

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