Bicyclic oriented graphs with skew-rank 6

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• 作者：Yong Lu ^{luyong.gougou@163.com" class="auth_mail" title="E-mail the corresponding author} ; Ligong Wang ; ^{lgwangmath@163.com" class="auth_mail" title="E-mail the corresponding author} ; ^{lgwang@nwpu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Qiannan Zhou ^{crabzhou1234@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Oriented graph ; Skew-rank ; Skew-adjacency matrix ; Bicyclic oriented graph
• 刊名：Applied Mathematics and Computation
• 出版年：2015
• 出版时间：1 November 2015
• 年：2015
• 卷：270
• 期：Complete
• 页码：899-908
• 全文大小：1003 K

文摘

Let G^σ be an oriented graph and S(G^σ) be its skew-adjacency matrix. The skew-rank of G^σ, denoted by sr(G^σ), is the rank of S(G^σ). In this paper, we characterize all the bicyclic oriented graphs with skew-rank 6. Let G^σ   be a bicyclic oriented graph with pendant vertices but no pendant twins. If sr(Gσ)=6,$sr\left(G^{\sigma }\right)=6,$ then 6 ≤ |V(G^σ)| ≤ 10.