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In this paper we characterize the unique graph whose least eigenvalue attains the minimum among all connected graphs of fixed order and given number of cut edges. [ABSTRACT FROM AUTHOR]

Let G be a simple connected graph of order n with degree sequence ( d, d, ..., d). Denote ( t) = Σ d, ( m) = ( t)/ d and ( N) = Σ ( t), where α is a real number. Denote by λ( G) and µ( G) the spectral radius of the adjacency matrix and the Laplacian matrix of G, respectively. In this paper, we present some upper and lower bounds of λ( G) and µ( G) in terms of ( t), ( m) and ( N). Furthermore, we also characterize some extreme graphs which attain these upper bounds. These results theoretically improve and generalize some known results. [ABSTRACT FROM AUTHOR]

Let G be a connected graph of order n. The diameter of a graph is the maximum distance between any two vertices of G. In this paper, we will give some bounds on the diameter of G in terms of eigenvalues of adjacency matrix and Laplacian matrix, respectively. [ABSTRACT FROM AUTHOR]