Bounds for the (Laplacian) spectral radius of graphs with parameter
Let be a simple connected graph of order with degree sequence . Denote , and , where is a real number. Denote by and the spectral radius of the adjacency matrix and the Laplacian matrix of , respectively. In this paper, we present some upper and lower bounds of and in terms of , and . Furthermore, we also characterize some extreme graphs which attain these upper bounds. These results theoretically improve and generalize some known results.