Solution: Graph Valid Tree

To determine if an undirected graph is a valid tree, it must be connected and contain no cycles. The solution involves performing a depth-first search (DFS) starting from the first node, marking nodes as visited. If a previously visited node is encountered that is not the parent, a cycle exists, indicating the graph is not a tree. After the DFS, if any nodes remain unvisited, the graph is disconnected. The algorithm runs in O(V + E) time and O(V) space, where V is the number of vertices and E is the number of edges.