UMA 2022
In this work, we use the null decomposition of unicyclic graphs in order to show that the core-nilpotent decomposition of \(A(U)\), the adjacency matrix of a unicyclic graph \(U\), can be obtained directly from the unicyclic graph itself. In other words, we give two invertible matrices \(Q\) and \(K\), expressed in terms of some adjacency relations of \(U\), such that \(Q^{-1}A(U)Q\) is a \(2\times 2\) blocks diagonal matrix, whose first block is \(K\), a \(r\times r\) matrix such that \(rk(K) = rk(A(U)) = r\), and whose second block is a zero matrix.
Trabajo en conjunto con: Maikon Machado Toledo (Universidade Federal do Rio Grande do Sul), Gonzalo Molina (Universidad Nacional de San Luis) y Cristian Panelo (Universidad Nacional de San Luis).