@article{Lin2022, 
author = {Zhen Lin},
title = {On the sum of powers of the  Aα-eigenvalues of graphs},
year = {2022},
journal = {Mathematical Modelling and Control},
volume = {2},
number = {2},
pages = {55-64},
keywords = {majorization, Aα-matrix, Aα-eigenvalues},
url = {https://www.sciopen.com/article/10.3934/mmc.2022007},
doi = {10.3934/mmc.2022007},
abstract = {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 recently defined the  Aα-matrix of  G as  Aα(G)=αD(G)+(1−α)A(G). The graph invariant  Sαp(G) is the sum of the  p-th power of the  Aα-eigenvalues of  G for  12<α<1, which has a close relation to the  α-Estrada index. In this paper, we establish some bounds on  Sαp(G) and characterize the extremal graphs. In particular, we present some bounds on  Sαp(G) in terms of the degree sequences, order and size of  G by using majorization techniques. Moreover, we give lower and upper bounds for  Sαp(G) of a bipartite graph and characterize the extremal graphs.}
}