Spectral radius of digraphs with given dichromatic number

✍ Scribed by Huiqiu Lin; Jinlong Shu

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 237 KB
• Volume: 434
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2010.12.026

✦ Synopsis

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.