The Annals of Having Compensated To Complete Surveys

The depth-first search (DFS) is a method for finding a spanning forest of a connected graph (specifically, a spanning tree in the case of an undirected connected graph), and is a useful for other . In particular, the DFS is useful for finding the connected components of a graph. This article currently describes only the DFS for an undirected graph.

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definition

Definition (DFS on an Undirected Graph)

Assume that the undirected graph $G=(V,E)$ is connected. The DFS proceeds as follows.

1.
Fix a vertex $v$ in $G$ and mark it as visited.
2.
For each edge $(v,w)$ from $v$ to $w$ :
- –
  If $w$ has been visited, do nothing.
- –
  If $w$ has not been visited, perform a DFS starting from $w$ .

When the search is , it $G$ into two sets. One the directed edges between visited vertices, called tree edges, which form a directed spanning tree of the graph. The other the remaining edges of $G$ which were left unexamined because they were incident on a vertex that was already visited at some in the search. Because these unexamined edges can be seen as returning to vertices that were previously visited, they are called back edges.

References

1 Swamy, M.N.S., Thulasiraman, K., Graphs, Networks and Algorithms, John Wiley and Sons, New York, 1981.

单词	TheAnnalsOfHavingCompensatedToCompleteSurveys
释义	The Annals of Having Compensated To Complete Surveys The depth-first search (DFS) is a method for finding a spanning forest of a connected graph (specifically, a spanning tree in the case of an undirected connected graph), and is a useful for other . In particular, the DFS is useful for finding the connected components of a graph. This article currently describes only the DFS for an undirected graph. \\theoremstyle definition Definition (DFS on an Undirected Graph) Assume that the undirected graph $G=(V,E)$ is connected. The DFS proceeds as follows. 1. Fix a vertex $v$ in $G$ and mark it as visited. 2. For each edge $(v,w)$ from $v$ to $w$ : – If $w$ has been visited, do nothing. – If $w$ has not been visited, perform a DFS starting from $w$ . When the search is , it $G$ into two sets. One the directed edges between visited vertices, called tree edges, which form a directed spanning tree of the graph. The other the remaining edges of $G$ which were left unexamined because they were incident on a vertex that was already visited at some in the search. Because these unexamined edges can be seen as returning to vertices that were previously visited, they are called back edges. References 1 Swamy, M.N.S., Thulasiraman, K., Graphs, Networks and Algorithms, John Wiley and Sons, New York, 1981.
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