易叔勇, 尤利华. 无环的本原反对称带号有向图的局部基与基指数[J]. 华南师范大学学报(自然科学版), 2011, (1).
引用本文: 易叔勇, 尤利华. 无环的本原反对称带号有向图的局部基与基指数[J]. 华南师范大学学报(自然科学版), 2011, (1).
The local bases and bases of primitive anti-symmetric signed digraphs with no loops[J]. Journal of South China Normal University (Natural Science Edition), 2011, (1).
Citation: The local bases and bases of primitive anti-symmetric signed digraphs with no loops[J]. Journal of South China Normal University (Natural Science Edition), 2011, (1).

无环的本原反对称带号有向图的局部基与基指数

The local bases and bases of primitive anti-symmetric signed digraphs with no loops

  • 摘要: n阶无环的本原反对称带号有向图S的局部基lS(k), 得到了lS(k)maxn + l-1;n + k-1(这里l为S中最小奇圈的长), 给出了kl 时lS(k)n + k-1的一个极图,因此证明了n阶无环的本原反对称带号有向图的S的基指数l(S)2n-1, 给出了达到上界的极图.

     

    Abstract: Let S be a signed digraph, if the underlying digraph D(S) is symmetric, and each 2-cycle in S is negative, then S is called an anti-symmetric signed digraph. The local bases of primitive anti-symmetric signed digraphs with no loops of order n is studied, and the following conclusion is proved that lS(k)maxn + l-1, n + k-1, where l is the shortest length of odd cycles of S. The upper bound of the bases of primitive anti-symmetric signed digraphs with no loops of order n are also obtained, and it is shown that the above obtained upper bounds are sharp.

     

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