Open AccessGroup inverse matrix of the normalized Laplacian on subdivision networks
Author(s) -
Á. Carmona,
Margarida Mitjana Riera,
Enric Monsó
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.