Sharp bounds for the spectral radius of digraphs

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Let G = (V, E) be a digraph with n vertices and m arcs without loops and multiarcs. The spectral radius ρ (G) of G is the largest eigenvalue of its adjacency matrix. In this paper, the following sharp bounds on ρ (G) have been obtained.min {sqrt(t i+ t j+ ) : (v i , v j ) ∈ E} ≤ ρ (G) ≤ max {sqrt(t i+ t j+ ) : (v i , v j ) ∈ E}where G is strongly connected and t i+ is the average 2-outdegree of vertex v i . Moreover, each equality holds if and only if G is average 2-outdegree regular or average 2-outdegree semiregular. © 2008.

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Xu, G. H., & Xu, C. Q. (2009). Sharp bounds for the spectral radius of digraphs. Linear Algebra and Its Applications, 430(5–6), 1607–1612.

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