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 Aα(G)=αD(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.