Aα and Lα-spectral properties of spider graphs

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