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协助子图的术语

[英]help with terminology of subgraphs

原文 2010-02-25 21:45:45 7 1 terminology/ graph-theory

Is there a term to describe a graph who has only one subgraph that is strongly connected? 是否有一个术语来描述只有一个紧密相连的子图的图？ (I'm not even sure I'm using strongly connected correctly here). （我什至不确定我在这里是否使用了正确的牢固连接）。

eg. 例如。 {AB,BC} has only one subgraph and {AB,BC,DE} has two. {AB，BC}仅具有一个子图，{AB，BC，DE}具有两个子图。

Note that I'm not considering that the graph {AB,BC} has three subgraphs: {AB,BC} and {AB} and {BC}. 请注意，我没有考虑图{AB，BC}具有三个子图：{AB，BC}和{AB}以及{BC}。

please distinguish between undirected and directed if need be. 如果需要，请区分非定向和定向。

1 个解决方案

I think you mean a connected graph, the alternative being a ~~forest~~ disconnected graph. 我认为您的意思是连接图，替代方案是森林断开图。

From http://en.wikipedia.org/wiki/Connectivity_%28graph_theory%29 -- 从http://en.wikipedia.org/wiki/Connectivity_%28graph_theory%29-

A graph is called connected if every pair of distinct vertices in the graph can be connected through some path. 如果图中的每对不同顶点都可以通过某个路径连接，则该图称为“已连接”。 A directed graph is called weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph. 如果将所有有向边替换为无向边，则有向图称为弱连接，从而产生一个连通（无向）图。 It is connected if it contains a directed path from u to v or a directed path from v to u for every pair of vertices u,v. 如果对于每对顶点u，v，它都包含从u到v的定向路径或从v到u的定向路径，则表明已连接。 It is strongly connected or strong if it contains a directed path from u to v and a directed path from v to u for every pair of vertices u,v. 如果每对顶点u，v都包含从u到v的有向路径和从v到u的有向路径，则它是强连通的或强连通的。 The strong components are the maximal strongly connected subgraphs. 强成分是最大的强连通子图。