Spectral radius of digraphs with given dichromatic number

Abstract Let D be a digraph with vertex set V ( D ) . A partition of V ( D ) into k acyclic sets is called a k -coloring of D . The minimum integer k for which there exists a k -coloring of D is the dichromatic number χ ( D ) of the digraph D . Denote G n , k the set of the digraphs of order n with the dichromatic number k ≥ 2 . In this note, we characterize the digraph which has the maximal spectral radius in G n , k . Our result generalizes the result of [8] by Feng et al.

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