| 谭学忠,谭学功.含有多个圈的图的秩[J].数学年刊A辑,2014,35(5):533~542 |
| 含有多个圈的图的秩 |
| On the Rank of Multicyclic Graphs |
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| DOI： |
| 中文关键词: 含有多个圈的图,奇异图,秩 |
| 英文关键词:Multicyclic graph, Singular graph, Rank |
| 基金项目:中央高校基本科研业务费专项资金(No.12JNKY008) 湖北省自然科学基金(No.2011CDB088)的资助 |
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| 中文摘要: |
| 研究了含有多个圈的图的邻接矩阵的秩.将k(k≥2)条点不交的路,首和尾分别粘合得到的图称为Θ-图.用Γ(k-1)表示含有Θ-图作为导出子图的(k-1)-圈图的集合,而用C(η,k)表示含有n个顶点和k个边不交的圈的图的集合.确定了Γ(k-1)中秩等于5和6的图以及C(n,k)中秩等于4,5和6的图. |
| 英文摘要: |
| In this paper, the rank of multicyclic graphs is investigated. A Θ-graph is obtained
from k (k > 2) vertex-disjoint paths by identifying their initial and terminal vertices. The
set of (k ? 1)-cyclic graphs which contain a Θ-graph as an induced subgraph is denoted by
Γ(k ? 1). Denote by C(n, k) the set of cacti, i.e., the connected graphs with n vertices and
k edge-disjoint cycles. The authors characterize the graphs with rank 5 and 6 in Γ?(k ? 1)
and the graphs with rank 4–6 in C(n, k). |
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