@article{Lin2022, 
author = {Zhen Lin},
title = {On the sum of the largest        A          α      -eigenvalues of graphs},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {8},
pages = {15064-15074},
keywords = {Aα-matrix, sum of Aα-eigenvalues, energy, graph operation},
url = {https://www.sciopen.com/article/10.3934/math.2022825},
doi = {10.3934/math.2022825},
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 defined the        A          α      -matrix of a graph    G as        A          α        (  G  )  =  α  D  (  G  )  +  (  1  −  α  )  A  (  G  ). Let        S    k    (      A          α        (  G  )  ) be the sum of the    k largest eigenvalues of        A          α        (  G  ). In this paper, some bounds on        S    k    (      A          α        (  G  )  ) are obtained, which not only extends the results of the sum of the    k largest eigenvalues of the adjacency matrix and signless Laplacian matrix, but it also gives new bounds on graph energy.}
}