2013/05/01 by Jianping Li, Bo Zhou, Li, Jianping +1
Mathematics · #05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C50 #msc:15A18
paper · pdf · doi:10.48550/arxiv.1305.0201
arxiv created 2013/05/01 · arxiv updated 2013/05/02
We determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order n≥ 4, and thus we answer affirmatively the problem whether the unique digraph which achieves the minimum spectral radius among all strongly connected bicyclic digraphs of order n achieves the second minimum spectral radius among all strongly connected digraphs of order n for n≥ 4 proposed in [H. Lin, J. Shu, A note on the spectral characterization of strongly connected bicyclic digraphs, Linear Algebra Appl. 436 (2012) 2524--2530]. We also discuss the strongly connected bicyclic digraphs with small and large spectral radii respectively.