Resumen de Aα and Lα-spectral properties of spider graphs

Andre Brondani, Francisca Andrea Macedo França, Carla Silva Oliveira

• Let G be a graph with adjacency matrix A(G) and let D(G) be the diagonal matrix of the degrees of G. For every real α ∈ [0, 1], Nikiforov [21] and Wang et al. [26] defined the matrices Aα(G) and Lα(G), respectively, as Aα(G) = αD(G)+(1−α)A(G) and Lα(G) = αD(G)+(α − 1)A(G). In this paper, we obtain some relationships between the eigenvalues of these matrices for some families of graphs, a part of the Aα and Lα-spectrum of the spider graphs, and we display the Aα and Lα-characteristic polynomials when their set of vertices can be partitioned into subsets that induce regular subgraphs. Moreover, we determine some subfamilies of spider graphs that are cospectral with respect to these matrices.