Bicyclic oriented graphs with skew-rank 2 or 4

The skew-rank of oriented graph G ? , denoted by sr ( G ? ) , is the rank of the skew-adjacency matrix of G ? . The skew-rank is even since the skew-adjacency matrix is skew-symmetric. In this paper we characterize the bicyclic oriented graphs with skew-rank 2 or 4.

[1]  Jianming Zhu.  Oriented unicyclic graphs with the first ⌊n-92⌋ largest skew energies , 2012 .

[2]  Bolian Liu,et al.  On the nullity of bicyclic graphs , 2005 .

[3]  Xueliang Li,et al.  Complete solution to a conjecture on the maximal energy of unicyclic graphs , 2010, Eur. J. Comb..

[4]  Hanyuan Deng,et al.  Extremal Graph with Respect to Matching Energy for a Random Polyphenyl Chain 1 , 2015 .

[5]  Yongtang Shi,et al.  Matching energy of unicyclic and bicyclic graphs with a given diameter , 2015, Complex..

[6]  Hou Yaoping,et al.  Oriented unicyclic graphs with extremal skew energy , 2011, 1108.6229.

[7]  Yongtang Shi,et al.  Complete Solution to a Conjecture on the Fourth Maximal Energy Tree , 2011 .

[8]  Yongtang Shi,et al.  On a Conjecture about Tricyclic Graphs with Maximal Energy , 2013, 1312.0204.

[9]  Guang-Hui Xu,et al.  3-Regular digraphs with optimum skew energy , 2012 .

[10]  Xueliang Li,et al.  4-Regular oriented graphs with optimum skew energy , 2013 .

[11]  Kexiang Xu,et al.  The Minimal Matching Energy of (n; m)-Graphs with a Given Matching Number , 2015 .

[12]  Guang-Hui Xu.  Some inequalities on the skew-spectral radii of oriented graphs , 2012 .

[13]  Yongtang Shi,et al.  The Maximal Matching Energy of Tricyclic Graphs , 2014, 1409.2038.

[14]  Willem H. Haemers,et al.  Skew-adjacency matrices of graphs , 2012 .

[15]  Shuli Li,et al.  On the Minimal Energy of Trees With a Given Number of Vertices of Odd Degree , 2015 .

[16]  Bryan L. Shader,et al.  Skew Spectra of Oriented Graphs , 2009, Electron. J. Comb..

[17]  Yaoping Hou,et al.  Characteristic Polynomials of Skew-Adjacency Matrices of Oriented Graphs , 2011, Electron. J. Comb..

[18]  Gui-Xian Tian.  On the skew energy of orientations of hypercubes , 2011 .

[19]  Wasin So,et al.  The skew energy of a digraph , 2010 .

[20]  Cui Denglan,et al.  On the skew spectra of Cartesian products of graphs , 2013 .

[21]  Guang-Hui Xu,et al.  The characteristic polynomial and the matchings polynomial of a weighted oriented graph , 2012 .

[22]  Yongtang Shi,et al.  Complete solution to a problem on the maximal energy of unicyclic bipartite graphs , 2010, 1010.6129.

[23]  Xueliang Li,et al.  Skew Spectra of Oriented Bipartite Graphs , 2013, Electron. J. Comb..

[24]  R. Balakrishnan,et al.  Skew Spectrum of the Cartesian Product of an Oriented Graph with an Oriented Hypercube , 2013 .

[25]  Xueliang Li,et al.  The skew-rank of oriented graphs , 2014, 1404.7230.

[26]  Michael S. Cavers,et al.  Graphs with Large Distinguishing Chromatic Number , 2013, Electron. J. Comb..