无向图的一个距离不等式

An lnequality of Distance for Undirected Graph

对任一无向图Ｇ（Ｘ，Ｅ），顶点集Ｘ＝｛ｘ１，ｘ２，…，ｘｎ｝，任给三点ｘｉ，ｘｊ，ｘｋ，若两两之间有距离，则成立不等式ｄＧ（ｘｉ，ｘｊ）＋ｄＧ（ｘｉ，ｘｋ）＋ｄＧ（ｘｊ，ｘｋ）≤２ｎ－２．另外，还提出了一个有关的猜想．

G(X,E) is an undirected graph, X={x 1,x 2,…,x n}is a set of vertices . x i,x j,x k∈X,if the distances between each other exist,then  d G(x i,x j)+d G(x i,x k)+d G(x j,x k)≤2n-2.In addition, we still bring forword a guess.