无环的本原反对称带号有向图的局部基与基指数

基金项目:

国家自然科学基金项目;高等学校博士学科点专项科研基金项目

详细信息

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)max{n + 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.
- 本原 /
- 不可幂 /
- 反对称 /
- 带号有向图 /
- 基指数 /
- 局部基
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)max{n + 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.
- primitive /
- non-powerful /
- anti-symmetric /
- signed digraph /
- base /
- local base