2014/05/20 by Xiaolin Chen, Xueliang Li, Chen, Xiaolin +3
Chemistry · Computer Science · Mathematics · #05C20 #05C50 #05C90 #15A18 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Synthesis and Properties of Aromatic Compounds #math.CO #msc:05C20 #msc:05C50 #msc:05C90 #msc:15A18
paper · pdf · doi:10.48550/arxiv.1405.4972
16 pages, 2 figures
openalex publication_date 2014/05/20 · arxiv created 2014/06/12 · arxiv updated 2014/06/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let G be a graph with maximum degree Δ, and let Gσ be an oriented graph of G with skew adjacency matrix S(Gσ). The skew spectral radius ρs(Gσ) of Gσ is defined as the spectral radius of S(Gσ). The skew spectral radius has been studied, but only few results about its lower bound are known. This paper determines some lower bounds of the skew spectral radius, and then studies the oriented graphs whose skew spectral radii attain the lower bound √Δ. Moreover, we apply the skew spectral radius to the skew energy of oriented graphs, which is defined as the sum of the norms of all the eigenvalues of S(Gσ), and denoted by Es(Gσ). As results, we obtain some lower bounds of the skew energy, which improve the known lower bound obtained by Adiga et al.