Eigenvalues of ${\mathbf{L}}_{\mathbf{\alpha }}-$matrices under graph operations

Gabriel Roberto Silva de Lima, Carla Silva Oliveira, João Domingos Gomes da Silva Junior

Let $G$ be a simple graph, $A(G)$ its adjacency matrix, and $D(G)$ its diagonal degree matrix. In 2022, \citeauthor{Wang2020} (\cite{Wang2020}) defined the family of matrices $L_{\alpha }$…