2021/05/07 by Haiying Shan, Feifei Wang, Shan, Haiying +3
Computer Science · Materials Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Magnetism in coordination complexes #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2105.03077
openalex publication_date 2021/05/07 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
In this paper, we characterize the extremal digraphs with the maximal or minimal α-spectral radius among some digraph classes such as rose digraphs, generalized theta digraphs and tri-ring digraphs with given size m. These digraph classes are denoted by Rmk, \widetilde\boldsymbolΘk(m) and \INF(m) respectively. The main results about spectral extremal digraph by Guo and Liu in \citeMR2954483 and Li and Wang in \citeMR3777498 are generalized to α-spectral graph theory. As a by-product of our main results, an open problem in \citeMR3777498 is answered. Furthermore, we determine the digraphs with the first three minimal α-spectral radius among all strongly connected digraphs. Meanwhile, we determine the unique digraph with the fourth minimal α-spectral radius among all strongly connected digraphs for 0≤ α≤ (1)/(2).