Some spectral properties of Aα-matrix
2019 ◽
Vol 11
(06)
◽
pp. 1950070
Keyword(s):
For a real number [Formula: see text], the [Formula: see text]-matrix of a graph [Formula: see text] is defined to be [Formula: see text] where [Formula: see text] and [Formula: see text] are the adjacency matrix and degree diagonal matrix of [Formula: see text], respectively. The [Formula: see text]-spectral radius of [Formula: see text], denoted by [Formula: see text], is the largest eigenvalue of [Formula: see text]. In this paper, we consider the upper bound of the [Formula: see text]-spectral radius [Formula: see text], also we give some upper bounds for the second largest eigenvalue of [Formula: see text]-matrix.