Super-Euler迭线图的特征刻划

图中端点度数不是２而内点的度数是２的路叫做枝。文中证明了一个连通图Ｇ的ｎ次迭线图Ｌ＾ｎ（Ｇ）是Ｓｕｐｅｒ－Ｅｕｌｅｒ图的充要条件是Ｇ有一个包含Ｇ的每个度至少为３的项点的子图Ｈ，满足：Ｈ的每个顶点都是偶度；Ｈ的孤立顶点在Ｇ中度至少为３；Ｈ的任何连通分支与Ｈ的其它连通分支在Ｇ中的距离至多是ｎ；对于Ｇ中不在Ｈ中的枝的长度至多为ｎ＋１，对于Ｇ中有端点度为１的枝的长度至多为ｎ。

Characterization of the n-th Super-eulerian Iterated Line Graph

A branch of a graph is a nontrivial path whose ends ha ve not degree 2 and whose internal vertices,if any,have degree 2.In this pa per,it is showed that the n-th iterated line graphL-n(G ) of a connected graph G is super-eulerian graph if and only if G contains a subgraph H which contains all the vertic es of degree at least 3,each of vertices of H have even degree in H,any isolated vertex of H has degree of at least 3 in G,the distance between any component of H and the ot hers in H is at most n,any branch of G which is not belong to H has length at most n+1,the legt h of any branch which has end of degree one is at most n.