Sesión Matemática DiscretaA Combinatorial core-nilpotent decomposition of unicyclic graphs
Micaela Vega
Universidad Nacional de San Luis - IMASL -CONICET, Argentina - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
A singular matrix \(A\) of rank \(r\) and order \(n\), is similar to a \(2\times 2\) block-diagonal, where one of the block a \(r\times r\) is non-singular matrix and the other block is nilpotent, see [1]. This is called a core-nilpotent decomposition of \(A\). In this work, we show that is possible to obtain a core-nilpotent decomposition of the adjacency matrix of a unicyclic graph throughout its adjacency relations, without computing a matrix \(Q\) (whose columns form a basis of the range and null space of the adjacency matrix of \(U\)) and its inverse. This is possible through the null decomposition of unicyclic graphs, see [2].
Trabajo en conjunto con: Daniel A Jaume ( Universidad Nacional de San Luis), Maikon Machado Toledo (Universidad Nacional de San Luis) y Cristian Panelo (Universidad Nacional de San Luis).
Referencias
[1] Meyer, C. Matrix Analysis and Applied Linear Algebra. Society for Industrial and Applied Mathematics (2000).
[2] Allem, L. E., Jaume, D. A., Molina, G., Toledo, M. M., and Trevisan, V., Null decomposition of unicyclic graphs, Discrete Applied Mathematics,(2020) 285:594-611.