On the generalized Aα-spectral characterizations of almost α-controllable graphs

作者：Li, Shuchao; Wang, Junming^*

来源：Discrete Mathematics, 2022, 345(8): 112913.

DOI：10.1016/j.disc.2022.112913

• Available online xxxx
• Generalized A alpha -spectrum
• Cospectral
• A alpha -matrix
• Walk matrix

The A alpha matrix of a graph G is defined by A alpha(G) = alpha D(G) + (1 - alpha)A(G), 0 < alpha < 1, where D(G) is the diagonal matrix of degrees and A(G) is the adjacency matrix of G. The A alpha-spectrum of a graph G, denoted by SpecA alpha (G), is the set of eigenvalues together with their multiplicities of A alpha(G). A graph G is said to be determined by the generalized A alpha-spectrum (DG A alpha S for short), if any graph H with SpecA alpha(G) = SpecA alpha(H) and SpecA alpha ( G over bar ) = SpecA alpha ( H over bar ), is isomorphic to G. In this paper, we present a simple arithmetic condition for an almost alpha-controllable graph being DG A alpha S, which generalizes the main results in [17].