Aα-spectral properties of some families of graphs with vertex connectivity equal to 1

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 [0, 1], Nikiforov [Applicable Analysis and Discrete Mathematics, 11(1): 81-107, 2017] defined the matrix A (G) by A (G) = D(G)+ (1-)A(G). In this paper, we obtain the eigenvalues of some families of graphs which have vertex connectivity equals to 1.