计算机问题求解一论题3-7 树 2018年10月16日
计算机问题求解 – 论题3-7 - 树 2018年10月16日
Theorem 4.1 An edge e of a graph G is a bridge if and only if e lies on no cycle of G. 推论：Every edge in a tree is a bridge 问题1g 从应用的角度看。上述推论有何 指导意义？
Theorem 4.1 An edge e of a graph G is a bridge if and only if e lies on no cycle of G. 推论：Every edge in a tree is a bridge
For an n-vertex graph G(with n 1),the following are equiv- alent(and characterize the trees with n vertices). A)G is connected and has no cycles. B)G is connected and has n-1 edges. C)G has n-1 edges and no cycles. D)For u,vE V(G),G has exactly one 4,v-path 问题2： 如何证明一系列命题等价？ 问题48 不能有回路对最小顶点度 数有什么影响？ 问题3：有n-1条边的n点连通图，一定是树？ 有n-1条边的无环连通图，一定连通n个点？
问题3：有n-1条边的n点连通图，一定是树？ 有n-1条边的无环连通图，一定连通n个点？
树的性质的“极限性” a)Every edge of a tree is a cut-edge. b)Adding one edge to a tree forms exactly one cycle. c)Every connected graph contains a spanning tree. 间题5： 什么样的图生成树是唯一的，为什么？ 如何构造一个连通图的生成树？
树的性质的“极限性
Merging Two Vertices V6
Merging Two Vertices v0 v6 v2 v5 v4 v1 v3 v6 v2 v5 v4 v3 v0 ’ v6 v5 v4 v3 v0