平均距离与色数

Mean distance and chromatic number

研究了n阶k色图中平均距离与色数的关系.在对n阶连通图中点距离和的一个结论证明基础之上,利用数学归纳法来研究平均距离与色数的关系.证明了平均距离与色数之间有一定关系.得到了n阶k色图中一点距离和的上界,并进一步给出了n阶k色图中平均距离的上界.

The relation between mean distance and chomatic number are analysed in the k-chromatic graph of order n. Based on the conclusion of the distance of a vertex by mean of the induction, there are relations between mean distance and chomatic number. A upper bound on the sum of distances of a vertex and mean distance in the k-chromatic graph of order n are gived in this paper.