TWO SHARP UPPER BOUNDS FOR THE SIGNLESS LAPLACIAN SPECTRAL RADIUS OF GRAPHS

Source abstract

The signless Laplacian matrix of a graph is the sum of its degree diagonal and adjacency matrices. In this paper, we present a sharp upper bound for the spectral radius of the adjacency matrix of a graph. Then this result and other known results are used to obtain two new sharp upper bounds for the signless Laplacian spectral radius. Moreover, the extremal graphs which attain an upper bound are characterized.