Let Gnk denote a set of graphs with n vertices and k cut edges. In this paper, we obtain an order of the first four graphs in Gnk in terms of their spectral radii for 6 ≤ k ≤ (n-2)/3.
A graph G is said to be determined by its Laplacian spectrum if any graph having the same Laplacian spectrum as G is isomorphic to G.We consider θ-graphs,that is,graphs obtained by subdividing the edges of the multigraph consist of three parallel edges.In this paper,some special θ-graphs are determined by their Laplacian spectra.
Let G(n,k,t) be a set of graphs with n vertices,k cut edges and t cut vertices.In this paper,we classify these graphs in G(n,k,t) according to cut vertices,and characterize the extremal graphs with the largest spectral radius in G(n,k,t).
