围绕割点的若干结论 Theorem 5.1 Let v be a vertex incident with a bridge in a connected graph G.Then v is a cut- vertex of G if and only if degv=2. Corollary 5.2 Let G be a connected graph of order 3 or more.If G contains a bridge,then G contains a cut-vertex. Theorem 5.3 Let v be a cut-vertex in a connected graph G and let u and w be vertices in distinct components of G-v.Then y lies on every u-w path in G. Corollary 5.4 A vertex v of a connected graph G is a cut-vertex of G if and only if there exist vertices u and w distinct from v such that v lies on every u-w path of G. Theorem 5.5 Let G be a nontrivial connected graph and let ueV(G).Ifv is a vertex that is farthest from u in G,then v is not a cut-vertex of G.围绕割点的若干结论