The Aα-spread of a graph.

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]