A polyomino is an edge-connected union of cells in the planar
square lattice. Here we consider generalized linear polyominoes;
that is, the polyominoes supported by an n Ã— 2 lattice. In this
paper, we obtain the Green function and the Kirchhoff index of a
generalized linear polyomino as a perturbation of a 2n-path by adding
weighted edges between opposite vertices. This approach deeply links
generalized linear polyomino Green functions with the inverse M-matrix
problem, and especially...
A polyomino is an edge-connected union of cells in the planar
square lattice. Here we consider generalized linear polyominoes;
that is, the polyominoes supported by an n Ã— 2 lattice. In this
paper, we obtain the Green function and the Kirchhoff index of a
generalized linear polyomino as a perturbation of a 2n-path by adding
weighted edges between opposite vertices. This approach deeply links
generalized linear polyomino Green functions with the inverse M-matrix
problem, and especially with the so-called Green matrices.
A polyomino is an edge-connected union of cells in the planar
square lattice. Here we consider generalized linear polyominoes; that is, the polyominoes supported by an n Ã— 2 lattice. In this paper, we obtain the Green function and the Kirchhoff index of a generalized linear polyomino as a perturbation of a 2n-path by adding weighted edges between opposite vertices. This approach deeply links generalized linear polyomino Green functions with the inverse M-matrix
problem, and especially with the so-called Green matrices.
Citation
Carmona, A., Encinas, A., Mitjana, M. Green matrices associated with generalized linear polyominoes. "Linear algebra and its applications", 2015, vol. 468, p. 38-47.