What is the difference between graph search and tree search?

Question

What is the difference between graph search and tree search versions regarding DFS, A* searches in artificial intelligence?

Answer 1

The only difference between a graph and a tree is cycle. A graph may contain cycles, a tree cannot. So when you're going to implement a search algorithm on a tree, you don't need to consider the existence of cycles, but when working with an arbitrary graph, you'll need to consider them. If you don't handle the cycles, the algorithm may eventually fall in an infinite loop or an endless recursion.

Another point to think is the directional properties of the graph you're dealing with. In most cases we deal with trees that represent parent-child relationships at each edge. A DAG (directed acyclic graph) also shows similar characteristics. But bi-directional graphs are different. Each edge in a bi-directional graphs represents two neighbors. So the algorithmic approaches should differ a bit for these two types of graphs.