On the Aα- spectral radius of Halin graphs

Abstract

For any real number α∈[0,1] and a graph G, Nikiforov [20] defined matrix Aα(G) asAα(G)=αD(G)+(1−α)A(G). The Aα- spectral radius of G is the largest eigenvalue of Aα(G). In this paper, we determine the first three largest extremal graphs in Halin graphs by their Aα- spectral radii when 12≤α<1. For 0≤α≤1, the 3-regular Halin graph alone minimizes the Aα- spectral radius for Halin graphs.