On the A_α spectral radius and A_α energy of non-strongly connected digraphs

2021/09/01 by Yang, Xiuwen, Wang, Ligong
#05C20 #05C50 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.00409

Abstract

Let A_α(G) be the A_α-matrix of a digraph G and λ_α1, λ_α2, …, λ_αn be the eigenvalues of A_α(G). Let ρ_α(G) be the A_α spectral radius of G and E_α(G)=∑_i=1ⁿ λ_αi² be the A_α energy of G by using second spectral moment. Let G_n^m be the set of non-strongly connected digraphs with order n, which contain a unique strong component with order m and some directed trees which are hung on each vertex of the strong component. In this paper, we characterize the digraph which has the maximal A_α spectral radius and the maximal (minimal) A_α energy in G_n^m.

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