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Check If Given Undirected Graph is a tree
Objective: Given an undirected graph, Write an algorithm to determine whether its tree or not.
An undirected graph is a tree if it has properties mentioned below
 There is no cycle present in the graph.
 The graph is connected. (All the vertices in the graph are connected)
Example:
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Approach:
Do DFS from any vertex. (please read DFS here), During DFS, for any current vertex X (currently visiting vertex) if there an adjacent vertex Y is present which is already visited and Y is not a direct parent of X then there is a cycle in the graph. If Cycle is present that means the graph is not a tree. If the cycle is not present then check whether the graph is connected. No need to do the DFS again to determine that, use the visited[] array filled during checking the cycle, if all the vertices are true in visited[] array means graph is connected and graph is tree else graph is not the tree.
Code:
Output:
Vertex connected from vertex: 0 >1 Vertex connected from vertex: 1 >3>0 Vertex connected from vertex: 2 >3 Vertex connected from vertex: 3 >4>2>1 Vertex connected from vertex: 4 >3 Given Graph is Tree  Vertex connected from vertex: 0 >4>1 Vertex connected from vertex: 1 >3>0 Vertex connected from vertex: 2 >3 Vertex connected from vertex: 3 >4>2>1 Vertex connected from vertex: 4 >0>3 Given Graph is not Tree  Vertex connected from vertex: 0 >1 Vertex connected from vertex: 1 >3>0 Vertex connected from vertex: 2 >3 Vertex connected from vertex: 3 >2>1 Vertex connected from vertex: 4 Given Graph is not Tree
Reference: GeeksforGeeks
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