A BOUND FOR THE Aα-SPECTRAL RADIUS OF A CONNECTED GRAPH AFTER VERTEX DELETION

作者：Wang, Chunxiang; She, Tao^*

来源：RAIRO-OPERATIONS RESEARCH, 2022, 56(5): 3635-3642.

DOI：10.1051/ro/2022176

• Spectral radius
• eigenvalue
• eigenvector
• adjacency matrix

G is a simple connected graph with adjacency matrix A(G) and degree diagonal matrix D(G). The signless Laplacian matrix of G is defined as Q(G) = D(G) + A(G). In 2017, Nikiforov [1] defined the matrix A(alpha)(G) = alpha D(G) + (1 - alpha)A(G) for alpha is an element of [0,1]. The A(alpha)-spectral radius of G is the maximum eigenvalue of A(alpha)(G). In 2019, Liu et al. [2] defined the matrix Theta(k)(G) as Theta(k)(G) = kD(G) + A(G), for k is an element of R. In this paper, we present a new type of lower bound for the A(alpha)-spectral radius of a graph after vertex deletion. Furthermore, we deduce some corollaries on Theta(k)(G), A(G), Q(G) matrices.