DFS-new-handouts-2

# DFS-new-handouts-2 - Depth-First Search 1:40 AM Depth-First...

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Depth-First Search 3/13/2006 1:40 AM 1 Depth-First Search 1 Depth-First Search D B A C E Depth-First Search 2 Outline and Reading Definitions (§6.1) ± Subgraph ± Connectivity ± Spanning trees and forests Depth - first search (§6.3.1) ± Algorithm ± Example ± Properties ± Analysis Applications of DFS (§6.5) ± Path finding ± Cycle finding

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Depth-First Search 3/13/2006 1:40 AM 2 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 3/13/2006 1:40 AM 3 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 applications to the design of communication networks A spanning forest of a graph is a spanning subgraph that is a forest Graph Spanning tree

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## This note was uploaded on 09/10/2009 for the course CS 401 taught by Professor Cs401 during the Spring '08 term at Illinois Tech.

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DFS-new-handouts-2 - Depth-First Search 1:40 AM Depth-First...

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