线图和有向线图的第二等周点连通度

摘要

证明了最小度大于等于2 的强连通有向线图的第二等周点连通度等于它的点连通度.对于无向线图, 给出了第二等周点连通度存在的充要条件,并且证明了在第二等周点连通度存在的前提下它或者等于限制点连通度或者等于d1+d2, 其中d1和d2分别是最小和次小度.%In this paper, we show that the second isoperimetric connectivity of strongly connected line digraphs with δ≥ equals its connectivity. For line graphs, we give a sufficient and necessary condition for the existence of the second isoperimetric connectivity, and we show that under the condition that the second isoperimetric connectivity exists, the second isoperimetric connectivity equals either the restricted vertex connectivity or d1+d2, where d1 and d2 are the smallest and the second smallest degree respectively.