Solution to a problem on skew spectral radii of oriented graphs.

Let G be a simple graph, and let G σ be an oriented graph of G with skew adjacency matrix S ( G σ ) . The skew spectral radius ρ s ( G σ ) of G σ is defined as the spectral radius of S ( G σ ) . When G is an odd-cycle graph (no even cycle), Cavers et al. (2012) [4] showed that the skew spectral radius of G σ is the same for every orientation σ of G . They proposed a problem: If G is a connected graph and ρ s ( G σ ) is the same for all orientations σ of G , must G be an odd-cycle graph? In this paper, we solve this problem and give a positive answer. [ABSTRACT FROM AUTHOR]