Abstract
Let G be a digraph with adjacency matrix A(G). Let D(G) be the diagonal matrix with outdegrees of vertices of G. In this paper, we study the convex linear combinations of A(G) and D(G), defined as Aα(G)=αD(G)+(1−α)A(G),0≤α≤1. The largest modulus of the eigenvalues of Aα(G), is called the Aα spectral radius of G, denoted by λα(G). We establish some lower bounds on Δ+−λα(G) for strongly connected irregular digraphs with given maximum outdegree and some other parameters, where Δ+ is the maximum vertex outdegree of G.
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