Search

Let G be a simple graph and A(G) be the adjacency matrix of G. The eigenvalues of A(G) are referred to as the eigenvalues of G. In this paper, we characterize the graphs with the minimal least eigenvalue among all graphs whose complements are connected and have only two pendent vertices.

Let S n c be the set of all connected graph each of which is a complement of an n -vertex unicyclic graph. Li and Wang (2012) determined the graphs with the least signless Laplacian eignvalue among all the graphs of the complements of n -vertex trees. In this paper, as a continuance of it, the unique graph among S n c which minimizes the least signless Laplacian eigenvalue is identified.