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Upper Bounds on the Aα Spectral Radius of Irregular Weighted Digraphs
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Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number.Let A(D)be the adjacency matrix of D and W(D)=diag(w1+,w2,...,wn+).In this paper,we study the matrix Aα(D),which is defined as Aα(D)=αW(D)+(1-α)A(D),0≤α≤1.The spectral radius of Aα(D)is called the Aα spectral radius of D,denoted by λα(D).We obtain some upper bounds on the Aα spectral radius of strongly connected irregular weighted digraphs.
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