Cycle base

1, the adjacency tree graph T(G) of simple connected graph G is a complete graph if and only if base number of cycle ρ(G)=1 and the length of the cycle is three.

文献1给出了简单连通图G的邻接树图T(G)是完全图的充分必要条件是:G的圈基数ρ(G)=1且此回路的长度为3。

At the same time,we determine the minimum cycle bases of them.

在ew(G)≥5的条件下,研究在平面和射影平面上2-连通的外可平面图的圈基结构,给出在这两种平面上嵌入的最小圈基。

Then we show that there is a one-one correspondence between minimum cycle bases and the shortest noncontractible cycles.

研究了射影平面上2 连通图的圈基结构,并给出了在嵌入的边宽度ew(G)≥5时外可平面图的最小圈基结构,证明了最小圈基与最短不可收缩圈之间的一一对应性。