图Ｇ中的一个与Ｋ１，３同构的导出子图叫做Ｇ的一个爪。爪中的３次顶点叫该爪的爪心。Ｂ表示Ｇ中所有爪心构成的集合。本文将证明：设Ｇ是顶点数≥３的连通、局部连通图，如果Ｇ的爪心集合Ｂ是点独立集，且Ｇ－Ｂ是局部连通的，则Ｇ是完全圈可扩的。

In a graph G,a induced subgraph isomorphic to K 1,3  is called a claw of G.The vertex with degree 3 in a claw is called a claw centre.The set of claw centres of G is denoted by B. In this paper, we prove that if G is connected, locally connected graph on at least three vertices such that the set of claw centres B is independent, and if G-B is locally connected, then G is fully cycle extendable.