961
个编辑
更改
跳到导航
跳到搜索
第1行：
第1行： − 此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。+ − + − − A graph with edges colored to illustrate path H-A-B (green), closed path or walk with a repeated vertex B-D-E-F-D-C-B (blue) and a cycle with no repeated edge or vertex H-D-G-H (red). − − 一个边着色的图表示路 H-A-B (绿色)、闭路或重复顶点 B-D-E-F-D-C-B (蓝色)和无重复边或顶点 H-D-G-H (红色)的循环。 第13行：
第9行： − 在图论中，图的圈是一个非空轨迹，其中只有第一个和最后一个顶点是重复的顶点。有向图的有向圈是一个非空的有向轨迹，其中只有第一个和最后一个顶点是重复的顶点。+ 第21行：
第17行： − 没有圈的图称为无圈图。没有有向圈的有向图称为有向无环图图。没有圈的连通图称为树。+ − + − + 第35行：
第31行： − 让我们做一个图。电路是一个具有顶点序列的非空轨迹。+ + − + −
无编辑摘要
此词条由Jie翻译。
[[File:Graph cycle.svg|thumb| A graph with edges colored to illustrate path H-A-B (green), closed path or walk with a repeated vertex B-D-E-F-D-C-B (blue) and a cycle with no repeated edge or vertex H-D-G-H (red).]]
[[File:Graph cycle.svg|thumb| A graph with edges colored to illustrate path H-A-B (green), closed path or walk with a repeated vertex B-D-E-F-D-C-B (blue) and a cycle with no repeated edge or vertex H-D-G-H (red). 这是一个经过着色的图，用于说明路径H-A-B（绿色），闭合路径或具有重复顶点的路径B-D-E-F-D-C-B（蓝色）和无重复边或顶点的环H-D-G-H（红色）。]]
In graph theory, a cycle in a graph is a non-empty trail in which the only repeated vertices are the first and last vertices. A directed cycle in a directed graph is a non-empty directed trail in which the only repeated vertices are the first and last vertices.
In graph theory, a cycle in a graph is a non-empty trail in which the only repeated vertices are the first and last vertices. A directed cycle in a directed graph is a non-empty directed trail in which the only repeated vertices are the first and last vertices.
在图论中，图中的一个环是非空轨迹，其中唯一重复的顶点是第一个和最后一个顶点。有向图中的有向环是非空有向迹线，其中唯一重复的顶点是第一个和最后一个顶点。
A graph without cycles is called an acyclic graph. A directed graph without directed cycles is called a directed acyclic graph. A connected graph without cycles is called a tree.
A graph without cycles is called an acyclic graph. A directed graph without directed cycles is called a directed acyclic graph. A connected graph without cycles is called a tree.
不带有环的图称为无环图。不带有有向环的有向图称为有向无环图。没有环的连接图称为树。
== Definitions ==
== Definitions 定义 ==
=== Circuit, cycle ===
=== Circuit, cycle 回路，环 ===
* A '''circuit''' is a non-empty [[Path (graph theory)#Walk, trail, path|trail]] in which the first and last vertices are repeated.{{sfn|Bender|Williamson|2010|p=164}}
* A '''circuit''' is a non-empty [[Path (graph theory)#Walk, trail, path|trail]] in which the first and last vertices are repeated.{{sfn|Bender|Williamson|2010|p=164}}
Let be a graph. A circuit is a non-empty trail with a vertex sequence .
Let be a graph. A circuit is a non-empty trail with a vertex sequence .
* 回路是一条非空路径，其中第一个和最后一个顶点重复。设图G =（V，E，ϕ），回路是具有顶点序列（v1，v2，...，vn，v1）的非空路径（e1，e2，…，en）。
* A '''cycle''' or '''simple circuit''' is a circuit in which the only repeated vertices are the first and last vertices.{{sfn|Bender|Williamson|2010|p=164}}
* A '''cycle''' or '''simple circuit''' is a circuit in which the only repeated vertices are the first and last vertices.{{sfn|Bender|Williamson|2010|p=164}}
* 在一个环或简单回路中，唯一重复的顶点是起始点和最终点。
*The '''length''' of a circuit or cycle is the number of edges involved.
*The '''length''' of a circuit or cycle is the number of edges involved.
* 一个回路或环的长度指的是相关连边的数量。
=== Directed circuit, cycle ===
=== Directed circuit, cycle ===