1
Graph Traversal
Discrete Mathematics
Problems related to Graph
• Graph Traversal
• Topological Sort
• Spanning Tree
• Minimum Spanning Tree
• Shortest Path
Graph Traversal Algorithm
• To traverse a tree, we use tree traversal algorithms like
pre-order, in-order, and post-order to visit all the nodes
in a tree
• Similarly, graph traversal algorithm tries to visit all the
nodes it can reach.
•
If a graph is disconnected a graph traversal that begins at
•
If a graph is disconnected
,
a graph traversal that begins at
a node v will visit only a subset of nodes, that is, the
connected component containing v.
Two basic Traversal Algorithms
• Two basic graph traversal algorithms:
– Depth-first-search (DFS)
• After visit node v, DFS strategy proceeds along a path from
v as deeply into the graph as possible before backing up
– Breadth-first-search (BFS)
•
After visit node v BFS strategy visits every node adjacent to
•
After visit node v
,
BFS strategy visits every node adjacent to
v before visiting any other nodes
Depth-first search (DFS)
• From a given node v, it first visits itself. Then, recursively
visit its unvisited neighbours one by one.
DFS Example
•Start from v
3
v
v
3
v2
v3
1
v
2
2
v
1
v4
v
3
v5
G
2
v1
3v4
4
v5
5
x
x
x
xx
docsity.com
