^{1}School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, PR China

^{2}School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, P.R. China

Abstract

The skew energy of oriented graphs is defined as the sum of the norms of all the eigenvalues of the skew adjacency matrix. In this note, we obtain some upper bounds for the skew energy of any oriented graphs, which improve the known upper bound obtained by Adiga et al.

C. Adiga, R. Balakrishnan and W. So (2010). The skew energy of a digraph. Linear Algebra Appl.. 432, 1825-1835

2

M. Cavers, S. M. Cioab, S. Fallat, D. A. Gregory, W. H. Haemers, S. J. Kirkland, J. J. McDonald and M. Tsatsomeros (2012). Skew-adjacency matrices of graphs. Linear Algebra Appl.. 436, 4512-4529

3

P. Chen, G. Xu and L. Zhang (2013). Ordering the oriented unicyclic graphs whose skew-spectral radius is bounded by 2. J. Inequal. Appl.. 2013, 12

4

X. Li and H. Lian A survey on the skew energy of oriented graphs. arXiv: 1304.5707.

5

B. Shader and W. So (2009). Skew spectra of oriented graphs. Electron. J. Combin.. 16 (1), 6

6

G. Xu (2012). Some inequalities on the skew-spectral radii of oriented graphs. J. Inequal. Appl.. 2012, 13

7

G. Xu and S. Gong (2013). On oriented graphs whose skew spectral radii do not exceed 2. Linear Algebra Appl.. 439, 2878-2887

8

X. Chen, X. Li and H. Lian Lower bounds of the skew spectral radii and skew energy of oriented graphs. arxiv.org/abs/1405.4972.

9

I. Gutman (1974). Bounds for total¦Ð-electron energy. Chem. Phys. Lett.. 24, 283-285

10

J. H. Koolen, V. Moulton and I. Gutman (2000). Improving the McClelland inequality for total¦Ð-electron energy. Chem. Phys. Lett.. 320, 213-216

11

J. H. Koolen and V. Moulton (2001). Maximal energy graphs. Adv. Appl. Math.. 26, 47-52

12

B. Zhou (2004). Energy of a graph. MATCH Commun. Math. Comput. Chem.. (51), 111-118

13

B. Zhou, I. Gutman and T. Aleksic (2008). A note on Laplacian energy of graphs. MATCH Commun. Math. Comput. Chem.. 60, 441-446

14

G. Tian (2011). On the skew energy of orientations of hypercubes. Linear Algebra Appl.. 435, 2140-2149