控制迹与线图的泛圈性

Dominating Trails and Pancyclicity of Line Graph

设u与v是圈G中的两个任意给定的顶点,本文给出图中存在连接u和v的控制迹的一个充分条件.若图G的阶n≥5,又对一切xy∈B(G)都有d(x)+d(y)≥n,本文证明线图L(G)是点泛圈的,且可使得与任一点关连的各个图几乎一个套一个,即几乎是可扩充的.

For a graph G with two prescribed vertices u and v,we give a sufficient condition for the ex- istence of a dominating trall connecting u and v.We also prove that if G is a graph of order n≥5,such that d(x)+d(y)≥n for every xy∈R(G),then the line graph L(G) is vertex pancyclic and the cycles associated with each vertex can be chosen such that they are almost nested.