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A 2-connected graph G is minimally 2-connected if deleting any arbitrary chosen edge of G always leaves a graph which is not 2-connected. In this paper, we give sharp upper bounds for the Laplacian spectral radius of (minimally) 2-connected graphs with given size, and determine the corresponding extremal graphs. [ABSTRACT FROM AUTHOR]

In this paper, we study the least Q-eigenvalue of a non-bipartite hamiltonian graph, and determine all non-bipartite hamiltonian graphs whose least Q-eigenvalue attains the minimum among all non-bipartite hamiltonian graphs on n vertices. [ABSTRACT FROM AUTHOR]

Abstract: Let G be a simple connected graph on n vertices and m edges. Lima et al. (2011) in [2] posed the following conjecture on the least eigenvalue of the signless Laplacian of G: . In this paper we prove a stronger result: For any graph with n vertices and m edges, we have . [Copyright &y& Elsevier]

Abstract: Tricyclic graphs are connected graphs in which the number of edges equals the number of vertices plus two. In this paper, we determine the graph with the largest Laplacian spectral radius among all tricyclic graphs with vertices and pendant vertices. [Copyright &y& Elsevier]

Abstract: Bicyclic graphs are connected graphs in which the number of edges equals the number of vertices plus one. In this paper we determine the graph with the largest spectral radius among all bicyclic graphs with n vertices and diameter d. As an application, we give first three graphs among all bicyclic graphs on n vertices, ordered according to their spectral radii in decreasing order. [Copyright &y& Elsevier]

Abstract: In this paper, we determine graphs with the largest spectral radius among all the unicyclic and all the bicyclic graphs with n vertices and k pendant vertices, respectively. [Copyright &y& Elsevier]

Abstract: Connected graphs in which the number of edges equals the number of vertices plus one are called bicyclic graphs. In this paper, all bicyclic graphs whose second largest eigenvalue does not exceed 1 have been determined. [Copyright &y& Elsevier]

Let A (G) and D (G) be the adjacency matrix and the degree diagonal matrix of a graph G , respectively. For any real number α ∈ [ 0 , 1 ] , Nikiforov defined the A α -matrix of a graph G as A α (G) = α D (G) + (1 − α) A (G). The A α -spread of a graph is the difference between the largest eigenvalue and the smallest eigenvalue of the A α -matrix of the graph. In this paper, we obtain some new lower bounds on A α -spread and characterize the extremal graphs for certain cases, which extend the results of A -spread and Q -spread. Moreover, some graph operations on A α -spread are presented. [ABSTRACT FROM AUTHOR]