摘要: 设
G图是一个简单连通图,图
G的离心距离和定义为
![](https://image.hanspub.org/IMAGE/Edit_dbcef7ab-29e5-4978-8e09-bafa5d05ce77.png)
,其中
![](https://image.hanspub.org/IMAGE/Edit_4f1aabb0-41e7-4f97-b95c-d38559430d2f.png)
表示顶点
ν的离心率,
![](https://image.hanspub.org/IMAGE/Edit_fef72633-a3dc-4718-8388-0a58a2b4e095.png)
表示在图
G中顶点
ν到其它所有顶点的距离和。本文刻画了控制数为
γ且具有最大离心距离和的树的结构。该结论是若干已有成果的推广。
Abstract:
Let
G be a connected graph. The eccentric distance sum of graph
G is defined as
![](https://image.hanspub.org/IMAGE/Edit_dbcef7ab-29e5-4978-8e09-bafa5d05ce77.png)
, where
![](https://image.hanspub.org/IMAGE/Edit_4f1aabb0-41e7-4f97-b95c-d38559430d2f.png)
is the eccentricity of the vertex
ν and
![](https://image.hanspub.org/IMAGE/Edit_fef72633-a3dc-4718-8388-0a58a2b4e095.png)
is the sum of all distances from the vertex
ν. In this paper, we characterize the tree with domination number
γ and the maximal eccentric distance sum. Some known results have been extended.