Generalized inverse of the Laplacian matrix and some applications | Zendy

Iván Gutman | Zendy; Wen Xiao | Zendy

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Generalized inverse of the Laplacian matrix and some applications

Author(s) -

Iván Gutman,

Wen Xiao

Publication year - 2004

Publication title -

bulletin classe des sciences mathematiques et natturalles

Language(s) - English

Resource type - Journals

eISSN - 2406-0909

pISSN - 0561-7332

DOI - 10.2298/bmat0429015g

Subject(s) - resistance distance , inverse , laplacian matrix , mathematics , laplace operator , generalized inverse , matrix (chemical analysis) , graph , combinatorics , pure mathematics , mathematical analysis , chemistry , geometry , graph power , chromatography , line graph

The generalized inverse L† 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 rij = {L†)ii + (L†)jj — (L†)ij - (L†)ji is encountered; it is called resistance distance. Based on the results obtained for L† we prove some previously known and deduce some new properties of the resistance distance. .

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