On the Generalized Adjacency Spread of a Graph

For a simple finite graph G, the generalized adjacency matrix is defined as Aα(G)=αD(G)+(1−α)A(G),α∈[0,1], where A(G) and D(G) are respectively diagonal of vertex degrees. The Aα-spread G difference between largest eigenvalue smallest Aα(G). In this paper, we answer question posed in (Lin, Z.; Miao, L.; Guo, S. Bounds on graph. Electron. J. Linear Algebra 2020, 36, 214–227). Furthermore, show that path graph, Pn, has S(Aα) among all trees order n. We establish relationship S(A). obtain several bounds for S(Aα).