The Nordhaus-Gaddum type inequalities of Aα-matrix

Abstract For a real number α ∈ [0, 1], the Aα-matrix of a graph G is defined as A α ( G ) = α D ( G ) + ( 1 − α ) A ( G ) , where A(G) and D(G) are the adjacency matrix and diagonal degree matrix of G, respectively. The Aα-spectral radius of G, denoted by ρα(G), is the largest eigenvalue of Aα(G). In this paper, the Nordhaus–Gaddum type bounds for the Aα-spectral radius are considered.

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