Group inverse matrix of the normalized Laplacian on subdivision networks | Zendy

Ángeles Carmona Mejías | Zendy; Margarida Mitjana Riera | Zendy; Enrique P.J. Monsó Burgués | Zendy

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Group inverse matrix of the normalized Laplacian on subdivision networks

Author(s) -

Ángeles Carmona Mejías,

Margarida Mitjana Riera,

Enrique P.J. Monsó Burgués

Publication year - 2020

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm180420023c

Subject(s) - subdivision , mathematics , inverse , laplacian matrix , laplace operator , matrix (chemical analysis) , group (periodic table) , base (topology) , combinatorics , mathematical analysis , geometry , chemistry , materials science , archaeology , organic chemistry , composite material , history

In this paper we consider a subdivision of a given network and we show how the group inverse matrix of the normalized laplacian of the subdivision network is related to the group inverse matrix of the normalized laplacian of the initial given network. Our approach establishes a relationship between solutions of related Poisson problems on both structures and takes advantage on the properties of the group inverse matrix. As a consequence we get formulae for effective resistances and the Kirchhoff Index of the subdivision network expressed in terms of its corresponding in the base network. Finally, we study two examples where the base network are the star and the wheel, respectively.

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