# DFS - Depth-First Search 4/1/2003 8:39 AM Outline and...

This preview shows pages 1–2. Sign up to view the full content.

Depth-First Search 1 Depth-First Search D B A C E Depth-First Search 2 Outline and Reading Definitions (§12.1) ± Subgraph ± Connectivity ± Spanning trees and forests Depth-first search (§12.3.1) ± Algorithm ± Example ± Properties ± Analysis Applications of DFS ± Path finding ± Cycle finding Depth-First Search 3 Subgraphs A subgraph S of a graph G is a graph such that ± The vertices of S are a subset of the vertices of G ± The edges of S are a subset of the edges of G A spanning subgraph of G is a subgraph that contains all the vertices of G Subgraph Spanning subgraph Depth-First Search 4 Connectivity A graph is connected if there is a path between every pair of vertices A connected component of a graph G is a maximal connected subgraph of G Connected graph Non connected graph with two connected components Depth-First Search 5 Trees and Forests A (free) tree is an undirected graph T such that ± T is connected ± T has no cycles This definition of tree is different from the one of a rooted tree A forest is an undirected graph without cycles The connected components of a forest are trees Tree Forest Depth-First Search 6 Spanning Trees and Forests A spanning tree of a connected graph is a spanning subgraph that is a tree A spanning tree is not unique unless the graph is a tree Spanning trees have

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## DFS - Depth-First Search 4/1/2003 8:39 AM Outline and...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online