# The skew-rank of oriented graphs

@inproceedings{Li2014TheSO, title={The skew-rank of oriented graphs}, author={Xueliang Li and Guihai Yu}, year={2014} }

An oriented graph G σ is a digraph without loops and multiple arcs, where G is called the underlying graph of G σ . Let S( G σ ) denote the skew-adjacency matrix of G σ . The rank of the skew-adjacency matrix of G σ is called the skew-rank of G σ , denoted by sr( G σ ). The skew-adjacency matrix of an oriented graph is skew symmetric and the skew-rank is even. We consider the skew-rank of simple oriented graphs. Firstly, we give some preliminary results about the skew-rank. Secondly, we…

## 26 Citations

Skew-rank of an oriented graph in terms of matching number

- Mathematics
- 2016

Abstract An oriented graph G σ is a digraph without loops and multiple arcs, where G is called the underlying graph of G σ . Let S ( G σ ) denote the skew-adjacency matrix of G σ . The rank of S ( G…

Upper bound of skew energy of an oriented graph in terms of its skew rank

- MathematicsLinear Algebra and its Applications
- 2019

Abstract Let G σ be an oriented graph with skew adjacency matrix S ( G σ ) . The skew energy E s ( G σ ) of G σ is the sum of the norms of all eigenvalues of S ( G σ ) and the skew rank r s ( G σ )…

Relation between the skew-rank of an oriented graph and the rank of its underlying graph

- Computer Science, MathematicsEur. J. Comb.
- 2016

It is proved that s r ( G ? ) ? r (G ) + 2 d ( G ) for an oriented graph G ?, the oriented graphs G ? whose skew-rank attains the upper bound are characterized.

On the relationship between the skew-rank of an oriented graph and the rank of its underlying graph

- MathematicsLinear Algebra and its Applications
- 2018

Abstract An oriented graph G σ is a digraph without loops and multiple arcs, where G is the underlying graph of G σ . Let S ( G σ ) denote the skew-adjacency matrix of G σ , and A ( G ) be the…

Skew-rank of an oriented graph with edge-disjoint cycles

- Mathematics
- 2016

An oriented graph is a digraph without loops and multiple arcs, where is called the underlying graph of . Let denote the skew-adjacency matrix of . The rank of is called the skew-rank of , denoted by…

Bicyclic oriented graphs with skew-rank 6

- Computer Science, MathematicsAppl. Math. Comput.
- 2015

All the bicyclic oriented graphs with skew-rank 6 are characterized, which is to say, all graphs with pendant vertices but no pendant twins are characterized.

Bicyclic oriented graphs with skew-rank 2 or 4

- Mathematics, Computer ScienceAppl. Math. Comput.
- 2015

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…

Nullity of Hermitian-Adjacency Matrices of Mixed Graphs

- 2018

A mixed graph means a graph containing both oriented edges and undirected edges. The nullity of the Hermitian-adjacency matrix of a mixed graph G, denoted by ηH(G), is referred to as the multiplicity…

The rank of a signed graph in terms of the rank of its underlying graph

- Mathematics
- 2018

Abstract Let Γ = ( G , σ ) be a signed graph and A ( Γ ) be its adjacency matrix, where G is the underlying graph of Γ. The rank r ( Γ ) of Γ is the rank of A ( Γ ) . We know that for a signed graph…

On the relation between the H-rank of a mixed graph and the matching number of its underlying graph

- Mathematics
- 2018

Abstract A mixed graph is obtained by orienting some edges of G, where G is the underlying graph of . Let denote the Hermitian adjacency matrix of and m(G) be the matching number of G. The H-rank of…

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